Latest in math.lo

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A Nonseparable Invariant Extension of Lebesgue Measure -- A Generalized and Abstract ApproachAug 22 2019Here using some methods of combinatorial set theory, particularly the ones related to the construction of independent families of sets and some modified version of the notion of small sets originally introduced by Riecan, Riecan and Neubrunn, we give ... More
Good Fibrations through the Modal PrismAug 21 2019Homotopy type theory is a formal language for doing abstract homotopy theory -- the study of identifications. But in unmodified homotopy type theory, there is no way to say that these identifications come from identifying the path-connected points of ... More
On the growth rate of dichromatic numbers of finite subdigraphsAug 20 2019Chris Lambie-Hanson proved recently that for every function $ f:\mathbb{N}\rightarrow \mathbb{N} $ there is an $ \aleph_1 $-chromatic graph $ G $ of size $ 2^{\aleph_1} $ such that every $ (n+3) $-chromatic subgraph of $ G $ has at least $ f(n) $ vertices. ... More
A synthetic approach to Markov kernels, conditional independence, and theorems on sufficient statisticsAug 19 2019We develop Markov categories as a framework for synthetic probability and statistics, following work of Golubtsov as well as Cho and Jacobs. This means that we treat the following concepts in purely abstract categorical terms: conditioning and disintegration; ... More
Rates of convergence for iterative solutions of equations involving set-valued accretive operatorsAug 19 2019This paper studies proofs of strong convergence of various iterative algorithms for computing the unique zeros of set-valued accretive operators that also satisfy some weak form of uniform accretivity at zero. More precisely, we extract explicit rates ... More
Directed Homotopy in Non-Positively Curved SpacesAug 19 2019A semantics of concurrent programs can be given using precubical sets, in order to study (higher) commutations between the actions, thus encoding the "geometry" of the space of possible executions of the program. Here, we study the particular case of ... More
Effectivizing Lusin's TheoremAug 17 2019Lusin's Theorem states that, for every Borel-measurable function $\bf{f}$ on $\mathbb R$ and every $\epsilon>0$, there exists a continuous function $\bf{g}$ on $\mathbb R$ which is equal to $\bf{f}$ except on a set of measure $<\epsilon$. We give a proof ... More
A Gentzen-style monadic translation of Gödel's System TAug 16 2019We present a monadic translation of G\"odel's System T in the spirit of Gentzen's negative translation, allowing us to reveal various structures of terms of System T.
Generalisations of Stationarity, Closed and Unboundedness, and of Jensen's $\Box$Aug 16 2019The concepts of closed unbounded (club) and stationary sets are generalised to $\gamma$-club and $\gamma$-stationary sets, which are closely related to stationary reflection. We use these notions to define generalisations of Jensen's combinatorial principles ... More
Cardinal invariants of Haar null and Haar meager setsAug 15 2019Aug 19 2019A subset $X$ of a Polish group $G$ is \emph{Haar null} if there exists a Borel probability measure $\mu$ and a Borel set $B$ containing $X$ such that $\mu(gBh)=0$ for every $g,h \in G$. A set $X$ is \emph{Haar meager} if there exists a compact metric ... More
Cardinal invariants of Haar null and Haar meager setsAug 15 2019A ssubset $X$ of a Polish group $G$ is \emph{Haar null} if there exists a Borel probability measure $\mu$ and a Borel set $B$ containing $X$ such that $\mu(gBh)=0$ for every $g,h \in G$. A set $X$ is \emph{Haar meager} if there exists a compact metric ... More
Lifting recursive counterexamples to higher-order arithmeticAug 15 2019In classical computability theory, a recursive counterexample to a theorem shows that the latter does not hold when restricted to computable objects. These counterexamples are highly useful in the Reverse Mathematics program, where the aim of the latter ... More
Bootstraps, nets, and hierarchiesAug 15 2019Classification is at the heart of the scientific enterprise, from bacteria in biology to groups in mathematics. A central classification project in mathematical logic is motivated by Goedel's incompleteness theorems. Indeed, logical systems are classified ... More
On homeomorphisms of Cantor space that induce only the trivial Turing automorphismAug 15 2019To determine whether there is a nontrivial automorphism of the Turing degrees remains a major open problem of computability theory. Past results have limited how nontrivial automorphisms could possibly be, and ruled out that an automorphism might be induced ... More
Towers and clubsAug 14 2019We revisit several results concerning club principles and nonsaturation of the nonstationary ideal, attempting to improve them in various ways. So we typically deal with a (non necessarily normal) ideal $J$ extending the nonstationary ideal on a regular ... More
Adjoining only the things you want: a survey of Strong Chang's Conjecture and related topicsAug 14 2019We survey some old and new results on strong variants of Chang's Conjecture and related topics.
Adjoining only the things you want: a survey of Strong Chang's Conjecture and related topicsAug 14 2019Aug 16 2019We survey some old and new results on strong variants of Chang's Conjecture and related topics.
Properties of the connective implication in effect algebrasAug 14 2019Effect algebras form a formal algebraic description of the structure of the so-called effects in a Hilbert space which serves as an event-state space for effects in quantum mechanics. This is why effect algebras are considered as logics of quantum mechanics, ... More
The Power of the Weisfeiler-Leman Algorithm to Decompose GraphsAug 14 2019The Weisfeiler-Leman procedure is a widely-used approach for graph isomorphism testing that works by iteratively computing an isomorphism-invariant coloring of vertex tuples. Meanwhile, a fundamental tool in structural graph theory, which is often exploited ... More
Modelling socio-political competitionAug 13 2019This paper continues the investigation of the logic of competing theories, be they scientific, social, political etc. We introduce a many-valued, multi-type modal language which we endow with relational semantics based on enriched reflexive graphs, inspired ... More
The logic of vague categoriesAug 13 2019We introduce a complete many-valued semantics for basic normal lattice-based modal logic. This relational semantics is grounded on many-valued formal contexts from Formal Concept Analysis. We discuss an interpretation and possible applications of this ... More
Polarized relations at singulars over successorsAug 13 2019Erdos, Hajnal and Rado asked whether $\binom{\aleph_{\omega_1}}{\aleph_2}\rightarrow\binom{\aleph_{\omega_1}}{\aleph_0}_2$ and whether $\binom{\aleph_{\omega_1}}{\aleph_2}\rightarrow\binom{\aleph_{\omega_1}}{\aleph_1}_2$. We prove that both relations ... More
Piece selection and cardinal arithmeticAug 12 2019We study the effects of piece selection principles on cardinal arithmetic (Shelah style). As an application, we discuss questions of Abe and Usuba. In particular, we show that if $\lambda \geq 2^\kappa$, then (a) $I_{\kappa, \lambda}$ is not $(\lambda, ... More
Uniform logical proofs for Riesz representation theorem, Daniell-Stone theorem and Stone's representation theorem for probability algebrasAug 10 2019Riesz representation theorem, Daniell-Stone theorem for Daniell integrals and Stone's representation theorem for probability and measure algebras are three important classical results in analysis concerning existence of measures with certain properties. ... More
EXPSPACE-Completeness of the Logics K4xS5 and S4xS5 and the Logic of Subset Spaces, Part 2: EXPSPACE-HardnessAug 09 2019It is known that the satisfiability problems of the product logics K4xS5 and S4xS5 are NEXPTIME-hard and that the satisfiability problem of the logic SSL of subset spaces is PSPACE-hard. We improve these lower bounds for the complexity of these problems ... More
EXPSPACE-Completeness of the Logics K4xS5 and S4xS5 and the Logic of Subset Spaces, Part 1: ESPACE-AlgorithmsAug 09 2019It is known that the satisfiability problems of the product logics K4xS5 and S4xS5 and of the logic SSL of subset spaces are in N2EXPTIME. We improve this upper bound for the complexity of these problems by presenting ESPACE-algorithms for these problems. ... More
Representing Polish groupoids via metric structuresAug 08 2019We prove that every open $\sigma$-locally Polish groupoid $G$ is Borel equivalent to the groupoid of models on the Urysohn sphere $\mathbb{U}$ of an $\mathcal{L}_{\omega_1\omega}$-sentence in continuous logic. In particular, the orbit equivalence relations ... More
Disturbance Decoupling and Instantaneous Fault Detection in Boolean Control NetworksAug 08 2019The literature available on disturbance decoupling (DD) of Boolean control network (BCN) is built on a restrictive notion of what constitutes as disturbance decoupling. The results available on necessary and sufficient conditions are of limited applicability ... More
On Extensions of Partial IsomorphismsAug 08 2019In this paper we study a notion of HL-extension (HL standing for Herwig--Lascar) for a structure in a finite relational language $\mathcal{L}$. We give a description of all finite minimal HL-extensions of a given finite $\mathcal{L}$-structure. In addition, ... More
Almost Indiscernible Theories and Saturated Free AlgebrasAug 07 2019We extend the concept of "almost indiscernible theory" introduced by Pillay and Sklinos in arXiv:1409.8604 (which was itself a modernization and expansion of Baldwin and Shelah (Algebra Universalis, 1983)), to uncountable languages and uncountable parameter ... More
On double-membership graphs of models of Anti-FoundationAug 07 2019We answer some questions about graphs which are reducts of countable models of Anti-Foundation, obtained by considering the binary relation of double-membership $x\in y\in x$. We show that there are continuum-many such graphs, and study their connected ... More
A Note on the "Third Life of Quantum Logic"Aug 07 2019The purpose of this note is to discuss some of the questions raised by Dunn, J. Michael; Moss, Lawrence S.; Wang, Zhenghan in Editors' introduction: the third life of quantum logic: quantum logic inspired by quantum computing.
A Note on the Possibility of Self-Reference in MathematicsAug 07 2019In this paper we propose an interpretation for self-referential propositions in a "meta-model" N* of ZF. This meta-model N* is considered as an informal model of arithmetic that mathematicians often use when working with number theory. Specifically, we ... More
A game-theoretic proof of Shelah's theorem on labeled treesAug 07 2019We give a new proof of a theorem of Shelah which states that for every family of labeled trees, if the cardinality $\kappa$ of the family is much larger (in the sense of large cardinals) than the cardinality $\lambda$ of the set of labels, more precisely ... More
A Logic for Dually Hemimorphic Semi-Heyting Algebras and Axiomatic ExtensionsAug 07 2019Semi-Heyting algebras were introduced by the second-named author during 1983-85 as an abstraction of Heyting algebras. The first results on these algebras, however, were published only in 2008 (see [San08]). Three years later, in [San11], he initiated ... More
Generalized Lens Categories via functors $\mathcal{C}^{\rm op}\to\mathsf{Cat}$Aug 06 2019Aug 07 2019Lenses have a rich history and have recently received a great deal of attention from applied category theorists. We generalize the notion of lens by defining a category $\mathsf{Lens}_F$ for any category $\mathcal{C}$ and functor $F\colon \mathcal{C}^{\rm ... More
Generalized Lens Categories via functors $\mathcal{C}^{\rm op}\to\mathsf{Cat}$Aug 06 2019Lenses have a rich history and have recently received a great deal of attention from applied category theorists. We generalize the notion of lens by defining a category Lens_F for any category $\mathcal{C}$ and functor $F: \mathcal{C}^{\rm op}\to\mathsf{Cat}$, ... More
Superstability, noetherian rings and pure-semisimple ringsAug 06 2019We uncover a connection between the model-theoretic notion of superstability and that of noetherian rings and pure-semisimple rings. We obtain a characterization of noetherian rings via superstability of the class of left modules with embeddings. $\mathbf{Theorem.}$ ... More
Pseudo-finite sets, pseudo-o-minimalityAug 05 2019We give an example of a model of the common theory of o-minimal structures, in a given language, and an expansion of that model admitting the exact same one-variable definable sets with the latter admitting a definable, closed, bounded, and discrete subset ... More
NNIL-formulas revisited: universal models and finite model propertyAug 05 2019NNIL-formulas, introduced by Visser in 1983-1984 in a study of $\Sigma_1$-subsitutions in Heyting Arithmetic, are intuitionistic propositional formulas that do not allow nesting of implication to the left. The main results about these formulas were obtained ... More
Sometime a Paradox, Now Proof: Non-First-Order-izability of Yablo's ParadoxAug 05 2019Aug 15 2019Paradoxes are interesting puzzles in philosophy and mathematics, and they can be even more fascinating, when turned into proofs and theorems. For example, Liar's paradox can be translated into a propositional tautology, and Barber's paradox turns into ... More
Sometime a Paradox, Now Proof: Non-First-Order-izability of Yablo's ParadoxAug 05 2019Paradoxes are interesting puzzles in philosophy and mathematics, and they can be even more fascinating when turned into proofs and theorems. For example, Liar's paradox can be translated into a propositional tautology, and Barber's paradox into a first-order ... More
Lower consistency bounds for mutual stationarity with divergent cofinalities and limited coveringAug 04 2019We improve previous work on the consistency strength of mutually stationary sequences of sets concentrating on points with divergent cofinality building on previous work by Adolf, Cox and Welch. Specifically, we have greatly reduced our reliance on covering ... More
Effective Finite-Valued Approximations of General Propositional LogicsAug 03 2019Propositional logics in general, considered as a set of sentences, can be undecidable even if they have "nice" representations, e.g., are given by a calculus. Even decidable propositional logics can be computationally complex (e.g., already intuitionistic ... More
Chain Logic and Shelah's Infinitary LogicAug 03 2019For a cardinal of the form $\kappa=\beth_\kappa$, Shelah's logic $L^1_\kappa$ has a characterisation as the maximal logic above $\bigcup_{\lambda<\kappa} L_{\lambda, \omega}$ satisfying Strong Undefinability of Well Order (SUDWO). SUDWO is a strengthening ... More
Varieties of positive modal algebras and structural completenessAug 01 2019Positive modal algebras are the positive-subreducts of modal algebras. We prove that the variety of positive S4-algebras is not locally finite. On the other hand, the free one-generated positive S4-algebra is shown to be finite. Moreover, we describe ... More
A study of truth predicates in matrix semanticsAug 01 2019Abstract algebraic logic is a theory that provides general tools for the algebraic study of arbitrary propositional logics. According to this theory, every logic L is associated with a matrix semantics Mod*(L). This paper is a contribution to the systematic ... More
On the complexity of the Leibniz hierarchyAug 01 2019We prove that the problem of determining whether a finite logical matrix determines an algebraizable logic is complete for EXPTIME. The same result holds for the classes of order algebraizable, weakly algebraizable, equivalential and protoalgebraic logics. ... More
A computational glimpse at the Leibniz and Frege hierarchiesAug 01 2019In this paper we consider, from a computational point of view, the problem of classifying logics within the Leibniz and Frege hierarchies typical of abstract algebraic logic. The main result states that, for logics presented syntactically, this problem ... More
A logical and algebraic characterization of adjunctions between generalized quasi-varietiesAug 01 2019We present a logical and algebraic description of right adjoint functors between generalized quasi-varieties, inspired by the work of McKenzie on category equivalence. This result is achieved by developing a correspondence between the concept of adjunction ... More
Epimorphism surjectivity in varieties of Heyting algebrasAug 01 2019It was shown recently that epimorphisms need not be surjective in a variety K of Heyting algebras, but only one counter-example was exhibited in the literature until now. Here, a continuum of such examples is identified, viz. the variety generated by ... More
A note on ordinal exponentiation and derivatives of normal functionsAug 01 2019Michael Rathjen and the present author have shown that $\Pi^1_1$-bar induction is equivalent to (a suitable formalization of) the statement that every normal function has a derivative, provably in $\mathbf{ACA_0}$. In this note we show that the base theory ... More
Bounds on Continuous Scott RankAug 01 2019An analog of Nadel's effective bound for the continuous Scott rank of metric structures, developed by Ben Yaacov, Doucha, Nies, and Tsankov, will be established: Let $\mathscr{L}$ be a language of continuous logic with code $\hat{\mathscr{L}}$. Let $\Omega$ ... More
Equations and first-order theory of one-relator and word-hyperbolic monoidsJul 31 2019We investigate systems of equations and the first-order theory of one-relator monoids and of word-hyperbolic monoids. We describe a family of one-relator monoids of the form $\langle A\mid w=1\rangle$ with decidable Diophantine problem (i.e.\ decidable ... More
A refinement of the Ramsey hierarchy via indescribabilityJul 31 2019Aug 13 2019A subset $X$ of a cardinal $\kappa$ is Ramsey if for every partition $f:[X]^{<\omega}\to 2$ there is a set $H\subseteq X$ of cardinality $\kappa$ which is \emph{homogeneous} for $f$, meaning that $f\upharpoonright[H]^n$ is constant for each $n<\omega$. ... More
A refinement of the Ramsey hierarchy via indescribabilityJul 31 2019A subset $X$ of a cardinal $\kappa$ is Ramsey if for every partition $f:[X]^{<\omega}\to 2$ there is a set $H\subseteq X$ of cardinality $\kappa$ which is \emph{homogeneous} for $f$, meaning that $f\upharpoonright[H]^n$ is constant for each $n<\omega$. ... More
Complexity in Young's LatticeJul 31 2019We investigate the complexity of the partial order relation of Young's lattice. The definable relations are characterized by establishing the maximal definability property modulo the single automorphism given by conjugation; consequently, as an ordered ... More
Simplicity of the automorphism groups of generalised metric spacesJul 30 2019Tent and Ziegler proved that the automorphism group of the Urysohn sphere is simple and that the automorphism group of the Urysohn space is simple modulo bounded automorphisms. In this paper we extend their methods and prove simplicity for many homogeneous ... More
Quantale semantics of Lambek calculus with subexponential modalitiesJul 30 2019In this paper, we consider the polymodal version of Lambek calculus with subexponential modalities initially introduced by Kanovich, Kuznetsov, Nigam, and Scedrov and its quantale semantics. In our approach, subexponential modalities have an interpretation ... More
Quantale semantics of Lambek calculus with subexponential modalitiesJul 30 2019Aug 08 2019In this paper, we consider the polymodal version of Lambek calculus with subexponential modalities initially introduced by Kanovich, Kuznetsov, Nigam, and Scedrov and its quantale semantics. In our approach, subexponential modalities have an interpretation ... More
Concentration of measure, classification of submeasures, and dynamics of $L_{0}$Jul 29 2019Exhibiting a new type of measure concentration, we prove uniform concentration bounds for measurable Lipschitz functions on product spaces, where Lipschitz is taken with respect to the metric induced by a weighted covering of the index set of the product. ... More
Complex Golay Pairs up to Length 28: A Search via Computer Algebra and Programmatic SATJul 27 2019We use techniques from the fields of computer algebra and satisfiability checking to develop a new algorithm to search for complex Golay pairs. We implement this algorithm and use it to perform a complete search for complex Golay pairs of lengths up to ... More
Ultrafilters on singular cardinals of uncountable cofinalityJul 26 2019We prove that consistently there is a singular cardinal $\kappa$ of uncountable cofinality such that $2^\kappa$ is weakly inaccessible, and every regular cardinal strictly between $\kappa$ and $2^\kappa$ is the character of some uniform ultrafilter on ... More
Equivalence à la Mundici for lattice-ordered monoidsJul 26 2019We provide a generalization of Mundici's equivalence between unital Abelian lattice-ordered groups and MV-algebras: the category of unital commutative lattice-ordered monoids is equivalent to the category of MMV-algebras (for `Monoidal MV-algebras'). ... More
Simultaneously vanishing higher derived limitsJul 26 2019In 1988, Sibe Marde\v{s}i\'{c} and Andrei Prasolov isolated an inverse system $\mathbf{A}$ with the property that the additivity of strong homology on any class of spaces which includes the closed subsets of Euclidean space would entail that $\lim^n\mathbf{A}$ ... More
Extensional Higher-Order Paramodulation in Leo-IIIJul 26 2019Leo-III is an automated theorem prover for extensional type theory with Henkin semantics and choice. Reasoning with primitive equality is enabled by adapting paramodulation-based proof search to higher-order logic. The prover may cooperate with multiple ... More
The spectrum problem for Abelian l-groups and MV-algebrasJul 25 2019Aug 05 2019This paper deals with the problem of characterizing those topological spaces which are homeomorphic to the prime spectra of MV-algebras or Abelian l-groups. As a first main result, we show that a topological space $X$ is the prime spectrum of an MV-algebra ... More
The spectrum problem for Abelian l-groups and MV-algebrasJul 25 2019This paper deals with the problem of characterizing those topological spaces which are homeomorphic to the prime spectra of MV-algebras or Abelian l-groups. As a first main result, we show that a topological space $X$ is the prime spectrum of an MV-algebra ... More
Uniform Martin's conjecture, locallyJul 24 2019We show that part I of uniform Martin's conjecture follows from a local phenomenon, namely that if a non-constant Turing invariant function goes from the Turing degree $\boldsymbol x$ to the Turing degree $\boldsymbol y$, then $\boldsymbol x \le_T \boldsymbol ... More
How to introduce the connective implication in orthomodular posetsJul 24 2019Since orthomodular posets serve as an algebraic axiomatization of the logic of quantum mechanics, it is a natural question how the connective of implication can be defined in this logic. It should be introduced in such a way that it is related with conjunction, ... More
Semigroups, Projections, $κ$-domainsJul 24 2019We propose an extension of the classical notion of projection to semigroups and provide conditions under which a semigroup embeds in a complete lattice. We also introduce the new notion of a $\kappa$-domain and prove some useful separation results valid ... More
Free Kleene algebras with domainJul 24 2019First we identify the free algebras of the class of algebras of binary relations equipped with the composition and domain operations. Elements of the free algebras are pointed labelled finite rooted trees. Then we extend to the analogous case when the ... More
Hyperfiniteness of boundary actions of hyperbolic groupsJul 23 2019We prove that for every finitely generated hyperbolic group $G$, the action of $G$ on its Gromov boundary induces a hyperfinite equivalence relation.
The word problem for double categoriesJul 23 2019We solve the word problem for double categories by translating it to the word problem for 2-categories. This yields a quadratic algorithm deciding the equality of diagrams in a free double category. The translation is of interest in its own right since ... More
The word problem for double categoriesJul 23 2019Aug 18 2019We solve the word problem for free double categories without equations between generators by translating it to the word problem for 2-categories. This yields a quadratic algorithm deciding the equality of diagrams in a free double category. The translation ... More
The word problem for double categoriesJul 23 2019Jul 28 2019We solve the word problem for free double categories without equations between generators by translating it to the word problem for 2-categories. This yields a quadratic algorithm deciding the equality of diagrams in a free double category. The translation ... More
Solution of Equations Involving the Modular $j$ FunctionJul 23 2019Inspired by work done for systems of polynomial exponential equations, we study systems of equations involving the modular $j$ function. We show general cases in which these systems have solutions, and then we look at certain situations in which the modular ... More
Solutions of equations involving the modular $j$ functionJul 23 2019Aug 15 2019Inspired by work done for systems of polynomial exponential equations, we study systems of equations involving the modular $j$ function. We show general cases in which these systems have solutions, and then we look at certain situations in which the modular ... More
Splitting chains, tunnels and twisted sumsJul 23 2019We study splitting chains in $\mathscr{P}(\omega)$, that is, families of subsets of $\omega$ which are linearly ordered by $\subseteq^*$ and which are splitting. We prove that their existence is independent of axioms of $\mathsf{ZFC}$. We show that they ... More
A formula for systems of Boolean polynomial equations and applications to parametrized complexityJul 23 2019It is known a method for transforming a system of Boolean polynomial equations to a single Boolean polynomial equation with less variables. In this paper, we improve the method, and give a formula in the Boolean polynomial ring for systems of Boolean ... More
A formula for systems of Boolean polynomial equations and applications to computational complexityJul 23 2019Jul 26 2019It is known a method for transforming a system of Boolean polynomial equations to a single Boolean polynomial equation with less variables. In this paper, we improve the method, and give a formula in the Boolean polynomial ring for systems of Boolean ... More
The $k$-Dimensional Weisfeiler-Leman AlgorithmJul 22 2019In this note, we provide details of the $k$-dimensional Weisfeiler-Leman Algorithm and its analysis from Immerman-Lander (1990). In particular, we present an optimized version of the algorithm that runs in time $O(n^{k+1}\log n)$, where $k$ is fixed (not ... More
Examples of weak amalgamation classesJul 22 2019We present several examples of hereditary classes of finite structures satisfying the joint embedding property and the weak amalgamation property, but failing the cofinal amalgamation property. These include a continuum-sized family of classes of finite ... More
Resetting $α$-register machines and ZF$^{-}$Jul 22 2019We study the computational strength of resetting $\alpha$-register machines, a model introduced by P. Koepke. Specifically, we prove the following strengthening of another recent result of ours: For an exponentially closed ordinal $\alpha$, we have $L_{\alpha}\models$ZF$^{-}$ ... More
Monomialization of a quasianalytic morphismJul 22 2019We prove a monomialization theorem for mappings in general classes of infinitely differentiable functions that are called quasianalytic. Examples include Denjoy-Carleman classes (of interest in real analysis), the class of infinitely differentiable functions ... More
Partitioning a reflecting stationary setJul 19 2019We address the question of whether a reflecting stationary set may be partitioned into two or more reflecting stationary subsets, providing various affirmative answers in ZFC. As an application to singular cardinals combinatorics, we infer that it is ... More
Provenance Analysis for Logic and GamesJul 19 2019A model checking computation checks whether a given logical sentence is true in a given finite structure. Provenance analysis abstracts from such a computation mathematical information on how the result depends on the atomic data that describe the structure. ... More
Override and updateJul 19 2019Override and update are natural constructions for combining partial functions, which arise in various program specification contexts. We use an unexpected connection with combinatorial geometry to provide a complete finite system of equational axioms ... More
Rediscovered theorem of LuzinJul 18 2019In 1934 N. N. Luzin proved in his short (but dense) paper \textit{Sur la decomposition des ensembles} that every set $X\subseteq \mathbb{R}$ can be decomposed into two full, with respect to Lebesgue measure or category, subsets. We will try to (at least ... More
A note on the classification of Gamma factorsJul 18 2019One of the earliest invariants introduced in the study of finite von Neumann algebras is the property Gamma of Murray and von Neumann. In this note we prove that it is not possible to classify separable $\rm{II}_1$ factors satisfying the property Gamma ... More
Bounded homomorphisms and finitely generated fiber products of latticesJul 18 2019We investigate when fiber products of lattices are finitely generated and obtain a new characterization of bounded lattice homomorphisms onto finitely presented lattices and onto lattices satisfying Whitman's condition. Specifically, for lattice epimorphisms ... More
Degrees of Randomized ComputabilityJul 17 2019In this survey we discuss work of Levin and V'yugin on collections of sequences that are non-negligible in the sense that they can be computed by a probabilistic algorithm with positive probability. More precisely, Levin and V'yugin introduced an ordering ... More
19th century real analysis, forward and backwardJul 17 201919th century real analysis received a major impetus from Cauchy's work. Cauchy mentions variable quantities, limits, and infinitesimals, but the meaning he attached to these terms is not identical to their modern meaning. Some Cauchy historians work in ... More
On mathematical realism and the applicability of hyperrealsJul 16 2019Jul 30 2019We argue that Robinson's hyperreals have just as much claim to applicability as the garden variety reals. In a recent text, Easwaran and Towsner (ET) analyze the applicability of mathematical techniques in the sciences, and introduce a distinction between ... More
On mathematical realism and the applicability of hyperrealsJul 16 2019We argue that Robinson's hyperreals have just as much claim to applicability as the garden variety reals. In a recent text, Easwaran and Towsner (ET) analyze the applicability of mathematical techniques in the sciences, and introduce a distinction between ... More
A Canonical Model Proof of Strong Completeness for BQLJul 16 2019I prove using a canonical model construction that a simple extension of Visser's natural deduction system for Basic Propositional Logic is both sound and strongly complete with respect to Basic First-Order Logic (BQL). I utilize the canonical model construction ... More
Abstract categorial grammars with island constraints and effective decidabilityJul 16 2019A well-known approach to treating syntactic island constraints in the setting of Lambek grammars consists in adding specific bracket modalities to the logic. We adapt this approach to abstract categorial grammars (ACG). Thus we define bracketed (implicational) ... More
Time-Stamped Claim LogicJul 15 2019Jul 16 2019The main objective of this paper is to define a logic for reasoning about distributed time-stamped claims. Such a logic is interesting for theoretical reasons, i.e., as a logic per se, but also because it has a number of practical applications, in particular ... More
A note on local $ω$-consistency and reflectionJul 15 2019In this note we answer a question of R. Kaye and H. Kotlarski regarding the relationship between the schemata of local $\omega$-consistency $\omega\textsf{-}\mathsf{Con}(\mathsf{PA})$ and local reflection $\mathsf{Rfn}(\mathsf{PA})$ for Peano arithmetic ... More
Ordinal sums of triangular norms on a bounded latticeJul 15 2019The ordinal sum construction provides a very effective way to generate a new triangular norm on the real unit interval from existing ones. One of the most prominent theorems concerning the ordinal sum of triangular norms on the real unit interval states ... More