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The Provability of ConsistencyFeb 20 2019Provability semantics suggests well-principled notions of constructive truth and constructive falsity of classical sentences in Peano arithmetic PA. F is constructively true iff PA proves F. F is constructively false iff PA proves that for each x, there ... More
The dual of compact partially ordered spaces is a varietyFeb 19 2019In a recent paper (2018), D. Hofmann, R. Neves and P. Nora proved that the dual of the category of compact partially ordered spaces and monotone continuous maps is a quasi-variety - not finitary, but bounded by $\aleph_1$. An open question was: is it ... More
Set-theoretic aspects of accessible categoriesFeb 18 2019An accessible category is, roughly, a category with all sufficiently directed colimits, in which every object can be resolved as a directed system of "small" subobjects. Such categories admit a purely category-theoretic replacement for cardinality: the ... More
Approximations of Isomorphism and Logics with Linear-Algebraic OperatorsFeb 18 2019Invertible map equivalences are approximations of graph isomorphism that refine the well-known Weisfeiler-Leman method. They are parametrised by a number k and a set Q of primes. The intuition is that two graphs G and H which are equivalent with respect ... More
Uniform Yomdin-Gromov parametrizations and points of bounded height in valued fieldsFeb 18 2019We prove a uniform version of non-Archimedean Yomdin-Gromov parametrizations in a definable context with algebraic Skolem functions in the residue field. The parametrization result allows us to bound the number of F_q[t]-points of bounded degrees of algebraic ... More
Homotopy canonicity for cubical type theoryFeb 18 2019Cubical type theory provides a constructive justification of homotopy type theory and satisfies canonicity: every natural number is convertible to a numeral. A crucial ingredient of cubical type theory is a path lifting operation which is explained computationally ... More
Fraïssé limit via forcingFeb 17 2019Given a Fra\"{i}ss\'{e} class $\mathcal{K}$ and an infinite cardinal $\kappa,$ we define a forcing notion which adds a structure of size $\kappa$ using elements of $\mathcal{K}$, which extends the Fra\"{i}ss\'{e} construction in the case $\kappa=\omega.$ ... More
Normalization by Evaluation for Call-by-Push-Value and Polarized Lambda-CalculusFeb 16 2019We observe that normalization by evaluation for simply-typed lambda-calculus with weak coproducts can be carried out in a weak bi-cartesian closed category of presheaves equipped with a monad that allows us to perform case distinction on neutral terms ... More
On the order dimension of locally countable partial orderingsFeb 16 2019We show that the order dimension of the partial order of all finite subsets of $\kappa$ under set inclusion is ${\log}_{2}({\log}_{2}(\kappa))$ whenever $\kappa$ is an infinite cardinal. We also show that the order dimension of any locally countable partial ... More
Types by Need (Extended Version)Feb 15 2019A cornerstone of the theory of lambda-calculus is that intersection types characterise termination properties. They are a flexible tool that can be adapted to various notions of termination, and that also induces adequate denotational models. Since the ... More
Mice with finitely many Woodin cardinals from optimal determinacy hypothesesFeb 15 2019We prove the following result which is due to the third author. Let $n \geq 1$. If $\boldsymbol\Pi^1_n$ determinacy and $\Pi^1_{n+1}$ determinacy both hold true and there is no $\boldsymbol\Sigma^1_{n+2}$-definable $\omega_1$-sequence of pairwise distinct ... More
Immediately algebraically closed fieldsFeb 15 2019We consider two overlapping classes of fields, IAC and VAC, which are defined using valuation theory but which do not involve a distinguished valuation. Rather, each class is defined by a condition that quantifies over all possible valuations on the field. ... More
Finding the limit of incompleteness IFeb 15 2019In this paper, I examine the limit of incompleteness w.r.t. interpretation. I first define the notion "G\"{o}del's first incompleteness theorem ($\sf G1$ for short) holds for theory $T$". This paper is motivated by the following question: whether there ... More
Quantifier alternation in a class of recursively defined tree propertiesFeb 14 2019Alternating quantifier depth is a natural measure of difficulty required to express first order logical sentences. We define a sequence of first order properties on rooted, locally finite trees in a recursive manner, and provide rigorous arguments for ... More
Which is the least complex explanation? Abduction and complexityFeb 14 2019It may happen that for a certain abductive problem there are several possible explanations, not all of them mutually compatible. What explanation is selected and which criteria are used to select it? This is the well-known problem of the selection of ... More
Note on some misinterpretations of Gödel's incompleteness theoremsFeb 14 2019In this paper, I evaluate some formal and informal misinterpretations of G\"{o}del's incompleteness theorems from the literature and the folklore, as well as clarify some misunderstandings about G\"{o}del's incompleteness theorems based on the current ... More
Remarks on the strict order propertyFeb 14 2019A well-known theorem of Shelah asserts that a theory has $OP$ (the order property) if and only if it has $IP$ (the independence property) or $SOP$ (the strict order property). We give a mild strengthening of Shelah's theorem for classical logic and a ... More
Epimorphisms in varieties of square-increasing residuated structuresFeb 13 2019It is proved that epimorphisms are surjective in a variety K of square-increasing commutative residuated lattices (with or without involution), provided that each finitely subdirectly irreducible algebra A in K has two properties: (1) A is generated by ... More
Topological dynamics of Polish group extensionsFeb 13 2019We consider a short exact sequence $1\to H\to G\to K\to 1$ of Polish groups and consider what can be deduced about the dynamics of $G$ given information about the dynamics of $H$ and $K$. We prove that if the respective universal minimal flows $M(H)$ ... More
Mv-algebras And Partially Cyclically Ordered GroupsFeb 13 2019We prove that there exists a functorial correspondence between MV-algebras and partially cyclically ordered groups which are wound round of lattice-ordered groups. It follows that some results about cyclically ordered groups can be stated in terms of ... More
Truth-preservation under fuzzy pp-formulasFeb 13 2019How can non-classical logic contribute to the analysis of complexity in computer science? In this paper, we give a step towards this question, taking a logical model-theoretic approach to the analysis of complexity in fuzzy constraint satisfaction. We ... More
CSPs with Global Modular Constraints: Algorithms and Hardness via Polynomial RepresentationsFeb 13 2019We study the complexity of Boolean constraint satisfaction problems (CSPs) when the assignment must have Hamming weight in some congruence class modulo M, for various choices of the modulus M. Due to the known classification of tractable Boolean CSPs, ... More
Kalimullin Pair and Semicomputability in $α$-Computability TheoryFeb 12 2019We generalize some results on semicomputability by Jockusch \cite{jockusch1968semirecursive} to the setting of $\alpha$-Computability Theory. We define an $\alpha$-Kalimullin pair and show that it is definable in the $\alpha$-enumeration degrees $\mathcal{D}_{\alpha ... More
On prevarieties of logicFeb 11 2019It is proved that every prevariety of algebras is categorically equivalent to a "prevariety of logic", i.e., to the equivalent algebraic semantics of some sentential deductive system. This allows us to show that no nontrivial equation in the language ... More
Singly generated quasivarieties and residuated structuresFeb 11 2019A quasivariety K of algebras has the joint embedding property (JEP) iff it is generated by a single algebra A. It is structurally complete iff the free countably generated algebra in K can serve as A. A consequence of this demand, called "passive structural ... More
A $\square(κ)$-like principle consistent with weak compactnessFeb 11 2019Sun proved that when $\kappa$ is weakly compact, the \emph{$1$-club} subsets of $\kappa$ provide a filter base for the weakly compact ideal, and hence can also be used to give a characterization of weakly compact sets which resembles the definition of ... More
Ekeland's variational principle in weak and strong systems of arithmeticFeb 11 2019We analyze Ekeland's variational principle in the context of reverse mathematics. We find that that the full variational principle is equivalent to $\Pi^1_1$-${\sf CA}_0$, a strong theory of second-order arithmetic, while natural restrictions (e.g.~to ... More
All those EPPA classes (Strengthenings of the Herwig-Lascar theorem)Feb 11 2019In this paper we prove a general theorem showing the extension property for partial automorphisms (EPPA, also called the Hrushovski property) for classes of structures containing relations and unary functions, optionally equipped with a permutation group ... More
On the maximal minimal cube lengths in distinct DNF tautologiesFeb 09 2019Inspired by a recent article by Anthony Zaleski and Doron Zeilberger, we investigate the question of determining the largest k for which there exists boolean formulas in disjunctive normal form (DNF) with n variables, none of whose conjunctions are `parallel', ... More
Approximation of subsets of natural numbers by c.e. setsFeb 09 2019The approximation of natural numbers subsets has always been one of the fundamental issues in computability theory. Computable approximation, $\Delta_2$-approximation, as well as introducing the generically computable sets have been some efforts for this ... More
The method of forcingFeb 08 2019The purpose of this article is to give a presentation of the method of forcing aimed at someone with a minimal knowledge of set theory and logic. The emphasis will be on how the method can be used to prove theorems in ZFC.
Graph-theoretic Simplification of Quantum Circuits with the ZX-calculusFeb 08 2019We present a new circuit-to-circuit optimisation routine based on an equational theory called the ZX-calculus. We first interpret quantum circuits as ZX-diagrams, a flexible, lower-level language for describing quantum computations graphically. Then, ... More
Representations in measure theory: between a non-computable rock and a hard to prove placeFeb 07 2019The development of measure theory in 'computational' frame-works like e.g. Reverse Mathematics, constructive mathematics, and computable analysis, proceeds by studying the computational properties of countable approximations of measurable objects. At ... More
The Cohomology of the Ordinals I: Basic Theory and Consistency ResultsFeb 07 2019In this paper, the first in a projected two-part series, we describe an organizing framework for the study of infinitary combinatorics. This framework is \v{C}ech cohomology. We show in particular that the \v{C}ech cohomology groups of the ordinals articulate ... More
Subset models for justification logicFeb 07 2019We introduce a new semantics for justification logic based on subset relations. Instead of using the established and more symbolic interpretation of justifications, we model justifications as sets of possible worlds. We introduce a new justification logic ... More
Coherence in Modal LogicFeb 07 2019A variety is said to be coherent if the finitely generated subalgebras of its finitely presented members are also finitely presented. In a recent paper by the authors it was shown that coherence forms a key ingredient of the uniform deductive interpolation ... More
On distributive join-semilatticesFeb 05 2019Motivated by Gentzen disjunction elimination rule in his Natural Deduction calculus and reading inequalities with meet in a natural way, we conceive a notion of distributivity for join-semilattices. We prove that it is equivalent to a notion present in ... More
The covering number of the strong measure zero ideal can be above almost everything elseFeb 05 2019We show that certain type of tree forcings, including Sacks forcing, increases the covering of the strong measure zero ideal $\mathcal{SN}$. As a consequence, in Sacks model, such covering number is equal to the size of the continuum, which indicates ... More
Descriptive Complexity of Computable Sequences RevisitedFeb 04 2019The purpose of this paper is to answer two questions left open in [B. Durand, A. Shen, and N. Vereshchagin, Descriptive Complexity of Computable Sequences, Theoretical Computer Science 171 (2001), pp. 47--58]. Namely, we consider the following two complexities ... More
Self-referentiality in Justification LogicFeb 04 2019The Logic of Proofs, LP, and other justification logics can have self-referential justifications of the form t:A. Such self-referential justifications are necessary for the realization of S4 in LP. Yu discovered prehistoric cycles in a particular Gentzen ... More
Maximal Tukey types, P-ideals and the weak Rudin-Keisler orderFeb 03 2019Feb 07 2019In this paper, we study some new examples of ideals on $\omega$ with maximal Tukey type (that is, maximal among partial orders of size continuum). This discussion segues into an examination of a refinement of the Tukey order -- known as the "weak Rudin-Keisler ... More
The number of languages with maximum state complexityFeb 02 2019Champarnaud and Pin (1989) found that the minimal deterministic automaton of a language $L\subset\Sigma^n$, where $\Sigma=\{0,1\}$, has at most \[ \sum_{i=0}^n \min(2^i, 2^{2^{n-i}}-1) \] states, and for each $n$ there exists $L$ attaining this bound. ... More
Planar digraphs for automatic complexityFeb 02 2019We show that the digraph of a nondeterministic finite automaton witnessing the automatic complexity of a word can always be taken to be planar. In the case of total transition functions studied by Shallit and Wang, planarity can fail. Let $s_q(n)$ be ... More
Truth and Feasible ReducibilityFeb 01 2019Let $\mathcal{T}$ be any of the three canonical truth theories $\textsf{CT}^-$ (Compositional truth without extra induction), $\textsf{FS}^-$ (Friedman--Sheard truth without extra induction), and $\textsf{KF}^-$ (Kripke--Feferman truth without extra induction), ... More
From non-commutative diagrams to anti-elementary classesFeb 01 2019Anti-elementarity is a strong way of ensuring that a class of structures , in a given first-order language, is not closed under elementary equivalence with respect to any infinitary language of the form $\mathscr{L}_{\infty\lambda}$. We prove that many ... More
Finite semantics of polymorphism, complexity and the power of type fixpointsFeb 01 2019Many applications of denotational semantics, such as higher-order model checking or the complexity of normalization, rely on finite semantics for monomorphic type systems. We present two constructions of finite semantics for second-order Multiplicative-Additive ... More
Completeness of infinitary heterogeneous logicJan 31 2019Given a regular cardinal $\kappa$ such that $\kappa^{<\kappa}=\kappa$ (e.g., if the Generalized Continuum Hypothesis holds), we develop a proof system for classical infinitary logic that includes heterogeneous quantification (i.e., infinite alternate ... More
Limiting Probability MeasuresJan 29 2019The coordinates along any fixed direction(s), of points on the sphere $S^{n-1}(\sqrt{n})$, roughly follow a standard Gaussian distribution as $n$ approaches infinity. We will revisit this classical result from a nonstandard perspective. We first develop ... More
Natural Density and The Quantifier MostJan 29 2019This paper considers the quantified simple sentences by \textit{Most}, sometimes referred to as proportional, sometimes the majority. The sentence form: \textit{Most A are B} where \textit{A} and \textit{B} are plural nouns. $ A $ and $ B $ range over ... More
Canonisation and Definability for Graphs of Bounded Rank WidthJan 29 2019We prove that the combinatorial Weisfeiler-Leman algorithm of dimension $(3k+4)$ is a complete isomorphism test for the class of all graphs of rank width at most $k$. Rank width is a graph invariant that, similarly to tree width, measures the width of ... More
Some results concerning the $\mathsf{SRT}^2_2$ vs. $\mathsf{COH}$ problemJan 29 2019The $\mathsf{SRT}^2_2$ vs.\ $\mathsf{COH}$ problem is a central problem in computable combinatorics and reverse mathematics, asking whether every Turing ideal that satisfies the principle $\mathsf{SRT}^2_2$ also satisfies the principle $\mathsf{COH}$. ... More
De Finettian Logics of Indicative ConditionalsJan 29 2019This paper explores trivalent truth conditions for indicative conditionals, examining the "defective" table put forward by de Finetti 1936, as well as Reichenbach 1944, first sketched in Reichenbach 1935. On their approach, a conditional takes the value ... More
Intuitionistic Non-Normal Modal Logics: A general frameworkJan 28 2019We define a family of intuitionistic non-normal modal logics; they can bee seen as intuitionistic counterparts of classical ones. We first consider monomodal logics, which contain only one between Necessity and Possibility. We then consider the more important ... More
LF groups, aec amalgamation, few automorphismsJan 28 2019In S. 1 we deal with amalgamation bases, e.g., we define when an a.e.c. $k$ has $(\lambda,\kappa)$-amalgamation which means "many" M in $K^k_\lambda$ are amalgamation bases. We then consider what happens for the class of lf groups. In S. 2 we deal with ... More
Categorical semantics of metric spaces and continuous logicJan 25 2019Using the category of metric spaces as a template, we develop a metric analogue of the categorical semantics of classical/intuitionistic logic, and show that the natural notion of predicate in this "continuous semantics" is equivalent to the a priori ... More
A consistency result on long cardinal sequencesJan 25 2019For any regular cardinal $\kappa$ and ordinal $\eta<\kappa^{++}$ it is consistent that $2^{\kappa}$ is as large as you wish, and every function $f:\eta \to [\kappa,2^{\kappa}]\cap Card$ with $f(\alpha)=\kappa$ for $cf(\alpha)<\kappa$ is the cardinal sequence ... More
A consistency result on long cardinal sequencesJan 25 2019Feb 18 2019For any regular cardinal $\kappa$ and ordinal $\eta<\kappa^{++}$ it is consistent that $2^{\kappa}$ is as large as you wish, and every function $f:\eta \to [\kappa,2^{\kappa}]\cap Card$ with $f(\alpha)=\kappa$ for $cf(\alpha)<\kappa$ is the cardinal sequence ... More
On a stronger reconstruction notion for monoids and clonesJan 24 2019Motivated by reconstruction results by Rubin, we introduce a new reconstruction notion for permutation groups, transformation monoids and clones, called automatic action compatibility, which entails automatic homeomorphicity. We further give a characterization ... More
On a stronger reconstruction notion for monoids and clonesJan 24 2019Feb 14 2019Motivated by reconstruction results by Rubin, we introduce a new reconstruction notion for permutation groups, transformation monoids and clones, called automatic action compatibility, which entails automatic homeomorphicity. We further give a characterization ... More
Ranks for families of theories and their spectraJan 24 2019We define ranks and degrees for families of theories, similar to Morley rank and degree, as well as Cantor-Bendixson rank and degree, and the notion of totally transcendental family of theories. Bounds for $e$-spectra with respect to ranks and degrees ... More
Approximations of theoriesJan 24 2019We study approximations of theories both in general context and with respect to some natural classes of theories. Some kinds of approximations are considered, connections with finitely axiomatizable theories and minimal generating sets of theories as ... More
Solving systems of equations in supernilpotent algebrasJan 23 2019Recently, M. Kompatscher proved that for each finite supernilpotent algebra $\mathbf{A}$ in a congruence modular variety, there is a polynomial time algorithm to solve polynomial equations over this algebra. Let $\mu$ be the maximal arity of the fundamental ... More
Directed Ramsey and Anti-Ramsey Algebras and the Flexible Atom ConjectureJan 21 2019We generalize the notion of a Ramsey algebra to directed graphs (asymmetric relations). We construct $m$-color Directed Anti-Ramsey algebras for $2\leq m \leq 1000$ (except for $m=8$). We also construct $m$-color Directed Ramsey algebras for various $m<500$. ... More
Relatively residuated lattices and posetsJan 20 2019It is known that every relatively pseudocomplemented lattice is residuated and, moreover, it is distributive. Unfortunately, non-distributive lattices with a unary operation satisfying properties similar to relative pseudocomplementation cannot be converted ... More
The Ramsey Theory of Henson graphsJan 20 2019For $k\ge 3$, the Henson graph $\mathcal{H}_k$ is the analogue of the Rado graph in which $k$-cliques are forbidden. Building on the author's result for $\mathcal{H}_3$, we prove that for each $k\ge 4$, $\mathcal{H}_k$ has finite big Ramsey degrees: To ... More
Tarski's relevance logicJan 19 2019Tarski's relevance logic is defined and shown to contain many formulas and derived rules of inference. The definition arises from Tarski's work on first-order logic restricted to finitely many variables. It is a relevance logic because it contains the ... More
Effective inseparability, lattices, and pre-ordering relationsJan 18 2019We study effectively inseparable (e.i.) pre-lattices (i.e. structures of the form $L=\langle \omega, \wedge, \lor, 0, 1, \leq_L\rangle$ where $\omega$ denotes the set of natural numbers and the following hold: $\wedge, \lor$ are binary computable operations; ... More
Definable V-topologies, Henselianity and NIPJan 17 2019We show that if $(K,v_1,v_2)$ is a bi-valued NIP field with $v_1$ henselian (resp. t-henselian) then $v_1$ and $v_2$ are comparable (resp. dependent). As a consequence Shelah's conjecture for NIP fields implies the henselianity conjecture for NIP fields. ... More
Stably Measurable CardinalsJan 16 2019We define a weak iterability notion that is sufficient for a number of arguments concerning $\Sigma_1$-definability at uncountable regular cardinals. In particular we give its exact consistency strength firstly in terms of the second uniform indiscernible ... More
Cohesive Powers of Linear OrdersJan 15 2019Cohesive powers of computable structures can be viewed as effective ultraproducts over effectively indecomposable sets called cohesive sets. We investigate the isomorphism types of cohesive powers $\Pi _{C}% \mathcal{L}$ for familiar computable linear ... More
Machine learning and the Continuum HypothesisJan 15 2019Jan 30 2019We comment on a recent paper that connects certain forms of machine learning to Set Theory. We point out that part of the set-theoretic machinery is related to a result of Kuratowski about decompositions of finite powers of sets and we show that there ... More
Near actionsJan 14 2019A near permutation of a set is a bijection between two cofinite subsets, modulo coincidence on smaller cofinite subsets. Near permutations of a set form its near symmetric group. In this monograph, we define near actions as homomorphisms into this group, ... More
Long range actions, connectedness, and dismantlability in relational structuresJan 14 2019In this paper we study alternative characterizations of dismantlability properties of relational structures in terms of various connectedness and mixing notions. We relate these results with earlier work of Brightwell and Winkler, providing a generalization ... More
Ramsey-like theorems and moduli of computationJan 14 2019Ramsey's theorem asserts that every $k$-coloring of $[\omega]^n$ admits an infinite monochromatic set. Whenever $n \geq 3$, there exists a computable $k$-coloring of $[\omega]^n$ whose solutions compute the halting set. On the other hand, for every computable ... More
Ramsey's CoheirsJan 14 2019We use the model theoretic notion of coheir to give short proofs of old and new theorems in Ramsey Theory. As an illustration we start from Ramsey's theorem itself. Then we prove Hindman's theorem and the Hales-Jewett theorem. Finally, we prove two Ramsey ... More
Topology is relevant (in the infinite-domain dichotomy conjecture for constraint satisfaction problems)Jan 14 2019The algebraic dichotomy conjecture for Constraint Satisfaction Problems (CSPs) of reducts of (infinite) finitely bounded homogeneous structures states that such CSPs are polynomial-time tractable when the model-complete core of the template has a pseudo-Siggers ... More
Continuous Regular FunctionsJan 10 2019Following Chaudhuri, Sankaranarayanan, and Vardi, we say that a function $f:[0,1] \to [0,1]$ is $r$-regular if there is a B\"{u}chi automaton that accepts precisely the set of base $r \in \mathbb{N}$ representations of elements of the graph of $f$. We ... More
Mechanization of Separation in Generic ExtensionsJan 10 2019We mechanize, in the proof assistant Isabelle, a proof of the axiom-scheme of Separation in generic extensions of models of set theory by using the fundamental theorems of forcing. We also formalize the satisfaction of the axioms of Extensionality, Foundation, ... More
On the Finiteness Problem for classes of modular latticesJan 10 2019The Finiteness Problem is shown to be unsolvable for any sufficiently large class of modular lattices.
On the nonexistence of Følner setsJan 08 2019We show that there is $n\in \mathbf N$, a finite system $\Sigma(\vec x,\vec y)$ of equations and inequations having a solution in some group, where $\vec x$ has length $n$, and $\epsilon>0$ such that: for any group $G$ and any $\vec a\in G^n$, if the ... More
Decision-making and Fuzzy Temporal LogicJan 07 2019There are moments where we make decisions involving tradeoffs among costs and benefits occurring in different times. Essentially, in these cases, we are evaluating dynamic processes with outcomes still unknown. So, do we use some intuitive logic to judge ... More
Effective embeddings for pairs of structuresJan 07 2019We study computable embeddings for pairs of structures, i.e. for classes containing precisely two non-isomorphic structures. We show that computable embeddings induce a non-trivial degree structure for two-element classes consisting of computable structures, ... More
The Complexity of Homomorphism FactorizationJan 07 2019We investigate the computational complexity of the problem of deciding if an algebra homomorphism can be factored through an intermediate algebra. Specifically, we fix an algebraic language, L, and take as input an algebra homomorphism f between two finite ... More
Distributive laws in residuated binarsJan 06 2019In residuated binars there are six non-obvious distributivity identities of $\cdot$,$/$,$\backslash$ over $\wedge, \vee$. We show that in residuated binars with distributive lattice reducts there are some dependencies among these identities; specifically, ... More
Relation algebras of Sugihara, Belnap, Meyer, ChurchJan 06 2019Sugihara's relation algebra is a complete atomic proper relation algebra that contains chains of relations isomorphic to Sugihara's original matrix. Belnap's relation algebra (better known as the Point Algebra) is a proper relation algebra containing ... More
Dense ideals and cardinal arithmeticJan 04 2019From large cardinals we show the consistency of normal, fine, $\kappa$-complete $\lambda$-dense ideals on $\mathcal{P}_\kappa(\lambda)$ for successor $\kappa$. We explore the interplay between dense ideals, cardinal arithmetic, and squares, answering ... More
Coherent forestsJan 04 2019A forest is a generalization of a tree, and here we consider the Aronszajn and Suslin properties for forests. We focus on those forests satisfying coherence, a local smallness property. We show that coherent Aronszajn forests can be constructed within ... More
Deciding the existence of minority termsJan 02 2019This paper investigates the computational complexity of deciding if a given finite idempotent algebra has a ternary term operation $m$ that satisfies the minority equations $m(y,x,x) \approx m(x,y,x) \approx m(x,x,y) \approx y$. We show that a common ... More
$R^{cl}(ω^2,3) = ω^6$Jan 01 2019We show that $R^{cl}(\omega^2,3) = \omega^6$.
Elimination of unknowns for systems of algebraic differential-difference equationsDec 29 2018We establish effective elimination theorems for differential-difference equations. Specifically, we find a computable function $B(r,s)$ of the natural number parameters $r$ and $s$ so that for any system of algebraic differential-difference equations ... More
Towards a Semantic Measure of the Execution Time in Call-by-Value lambda-Calculus (Long Version)Dec 27 2018We investigate the possibility of a semantic account of the execution time (i.e. the number of \beta_v-steps leading to the normal form, if any) for the shuffling calculus, an extension of Plotkin's call-by-value {\lambda}-calculus. For this purpose, ... More
Approximate counting and NP search problemsDec 27 2018We study a new class of NP search problems, those which can be proved total in the theory $\mathrm{APC}_2$ of [Je\v{r}\'abek 2009]. This is an axiomatic theory in bounded arithmetic which can formalize standard combinatorial arguments based on approximate ... More
Locally definable and approximate subgroups of semialgebraic groupsDec 27 2018We prove the following instance of a conjecture stated in arXiv:1103.4770. Let $G$ be an abelian semialgebraic group over a real closed field $R$ and let $X$ be a semialgebraic subset of $G$. Then the group generated by $X$ contains a generic set and ... More
Expansions of real closed fields which introduce no new smooth functionsDec 25 2018We prove the following theorem: let $\widetilde{\mathcal R}$ be an expansion of the real field $\overline{\mathbb R}$, such that every definable set (I) is a uniform countable union of semialgebraic sets, and (II) contains a "semialgebraic chunk". Then ... More
Combinatorial principles equivalent to weak inductionDec 24 2018We consider two combinatorial principles, ${\sf{ERT}}$ and ${\sf{ECT}}$. Both are easily proved in ${\sf{RCA}}_0$ plus ${\Sigma^0_2}$ induction. We give two proofs of ${\sf{ERT}}$ in ${\sf{RCA}}_0$, using different methods to eliminate the use of ${\Sigma^0_2}$ ... More
Residuated operators and Dedekind-MacNeille completionDec 22 2018The concept of operator residuation for bounded posets with unary operation was introduced by the first two authors. It turns out that in some cases when these operators are transformed into lattice terms and the poset ${\mathbf P}$ is completed into ... More
Residuation in modular lattices and posetsDec 22 2018We show that every complemented modular lattice can be converted into a left residuated lattice where the binary operations of multiplication and residuum are term operations. The concept of an operator left residuated poset was introduced by the authors ... More
Forking, Imaginaries and other features of ACFGDec 21 2018We study the generic theory of algebraically closed fields of fixed positive characteristic with a predicate for an additive subgroup, called $\mathrm{ACFG}$. This theory was introduced recently as a new example of $\mathrm{NSOP}_1$ non simple theory. ... More
Souslin trees at successors of regular cardinalsDec 20 2018We present a weak sufficient condition for the existence of Souslin trees at successor of regular cardinals. The result is optimal and simultaneously improves an old theorem of Gregory and a more recent theorem of the author.
Invariant hypersurfacesDec 20 2018The following theorem, which includes as very special cases results of Jouanolou and Hrushovski on algebraic $D$-varieties on the one hand, and of Cantat on rational dynamics on the other, is established: Working over a field of characteristic zero, suppose ... More