Latest in math.lo

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A syntactic approach to continuity of T-definable functionalsApr 22 2019We give a new proof of the well-known fact that all functions $(\mathbb{N} \to \mathbb{N}) \to \mathbb{N}$ which are definable in G\"odel's System T are continuous via a syntactic approach. Differing from the usual syntactic method, we firstly perform ... More
Compositionality of Rewriting Rules with ConditionsApr 19 2019We extend the notion of compositional associative rewriting as recently studied in the rule algebra framework literature to the setting of rewriting rules with conditions. Our methodology is category-theoretical in nature, where the definition of rule ... More
Cantor-Bernstein implies Excluded MiddleApr 19 2019We prove in constructive logic that the statement of the Cantor-Bernstein theorem implies excluded middle. This establishes that the Cantor-Bernstein theorem can only be proven assuming the full power of classical logic. The key ingredient is a theorem ... More
The incompleteness of an incompleteness argumentApr 18 2019G\"odel's argument for the First Incompleteness Theorem is, structurally, a proof by contradiction. This article intends to reframe the argument by, first, isolating an additional assumption the argument relies on, and then, second, arguing that the contradiction ... More
Logics for first-order team propertiesApr 18 2019In this paper, we introduce a logic based on team semantics, called FOT, whose expressive power coincides with first-order logic both on the level of sentences and (open) formulas, and we also show that a sublogic of FOT, called FOT${}^\downarrow$, captures ... More
Cubical Syntax for Reflection-Free Extensional EqualityApr 18 2019We contribute XTT, a cubical reconstruction of Observational Type Theory which extends Martin-L\"of's intensional type theory with a dependent equality type that enjoys function extensionality and a judgmental version of the unicity of identity types ... More
A unified framework for notions of algebraic theoryApr 18 2019Universal algebra uniformly captures various algebraic structures, by expressing them as equational theories or abstract clones. The ubiquity of algebraic structures in mathematics and related fields has given rise to several variants of universal algebra, ... More
Re-pairing bracketsApr 17 2019Consider the following one-player game. Take a well-formed sequence of opening and closing brackets. As a move, the player can pair any opening bracket with any closing bracket to its right, erasing them. The goal is to re-pair (erase) the entire sequence, ... More
The model theory of Cohen ringsApr 17 2019The aim of this article is to give an self-contained account of the algebra and model theory of Cohen rings, a natural generalization of Witt rings. Witt rings are only valuation rings in case the residue field is perfect, and Cohen rings arise as the ... More
A Comparison of Pair and Triple Partition RelationsApr 16 2019This paper considers three different partition relations from partition calculus, two of which are pair relations and one of which is a triple relation. An examination of the first partition relation and the ramification argument used to prove it will ... More
Completeness for Game LogicApr 16 2019Game logic was introduced by Rohit Parikh in the 1980s as a generalisation of propositional dynamic logic (PDL) for reasoning about outcomes that players can force in determined 2-player games. Semantically, the generalisation from programs to games is ... More
A short proof of Thoma's theorem on type I groupsApr 16 2019In the theory of unitary group representations, a group is called type I if all factor representations are of type I, and by a celebrated theorem of James Glimm [Gli61b], the type I groups are precisely those groups for which the irreducible unitary representations ... More
Combinatorial Conversion and Moment Bisimulation for Stochastic Rewriting SystemsApr 15 2019We develop a novel method to analyze the dynamics of stochastic rewriting systems evolving over finitary adhesive, extensive categories. Our formalism is based on the so-called rule algebra framework and exhibits an intimate relationship between the combinatorics ... More
A Linear Upper Bound on the Weisfeiler-Leman Dimension of Graphs of Bounded GenusApr 15 2019The Weisfeiler-Leman (WL) dimension of a graph is a measure for the inherent descriptive complexity of the graph. While originally derived from a combinatorial graph isomorphism test called the Weisfeiler-Leman algorithm, the WL dimension can also be ... More
Separation of bounded arithmetic using a consistency statementApr 14 2019This paper proves Buss's hierarchy of bounded arithmetics $S^1_2 \subseteq S^2_2 \subseteq \cdots \subseteq S^i_2 \subseteq \cdots$ does not entirely collapse. More precisely, we prove that, for a certain $D$, $S^1_2 \subsetneq S^{2D+5}_2$ holds. Further, ... More
On Loeb and sequential spaces in $\mathbf{ZF}$Apr 14 2019A topological space is called Loeb if the collection of all its non-empty closed sets has a choice function. In this article, in the absence of the axiom of choice, connections between Loeb and sequential spaces are investigated. Among other results, ... More
Axiomatizing first-order consequences in inclusion logicApr 12 2019Inclusion logic is a variant of dependence logic that was shown to have the same expressive power as positive greatest fixed-point logic. Inclusion logic is not axiomatizable in full, but its first-order consequences can be axiomatized. In this paper, ... More
Generalized topological semantics for weak modal logicsApr 12 2019The notion of \textit{general} or \textit{generalized} topology can be interpreted in many ways. In this paper, we shall adhere to the concept introduced by Cs\'{a}sz\'{a}r in \cite{csaszar}. Hence, we assume that generalized topology contains empty set ... More
Uniform Interpolation and Compact CongruencesApr 12 2019Uniform interpolation properties are defined for equational consequence in a variety of algebras and related to properties of compact congruences on first the free and then the finitely presented algebras of the variety. It is also shown, following related ... More
Implications of positive formulas in modules (RIMS)Apr 12 2019In this survey the role of implications of positive formulas -- finitary and infinitary -- is dicussed, in general and in module categories, where they seem of particular importance. A list of algebraic examples is given, some old, some rather new, and ... More
The Ramsey property implies no mad familiesApr 11 2019We show that if all collections of infinite subsets of $\N$ have the Ramsey property, then there are no infinite maximal almost disjoint (mad) families. This solves a long-standing problem going back to Mathias \cite{mathias}. The proof exploits an idea ... More
The Ramsey property implies no mad familiesApr 11 2019Apr 15 2019We show that if all collections of infinite subsets of $\N$ have the Ramsey property, then there are no infinite maximal almost disjoint (mad) families. This solves a long-standing problem going back to Mathias \cite{mathias}. The proof exploits an idea ... More
Definable maximal cofinitary groups of intermediate sizeApr 11 2019Using almost disjoint coding, we show that for each $1<M<N<\omega$ consistently $\mathfrak{d}=\mathfrak{a}_g=\aleph_M<\mathfrak{c}=\aleph_N$, where $\mathfrak{a}_g=\aleph_M$ is witnessed by a $\Pi^1_2$ maximal cofinitary group.
Weak factorization systems and stable independenceApr 11 2019We exhibit a bridge between the theory of weak factorization systems, a categorical concept used in algebraic topology and homological algebra, and the model-theoretic notion of stable independence. Roughly speaking, we show that the cofibrantly generated ... More
O-minimal de Rham cohomologyApr 11 2019In the present paper we elaborate an o-minimal de Rham cohomology theory for abstract-definable $\mathcal{C}^p$ manifolds with $1\leq p\leq \infty$ in an o-minimal expansion of the real field which admits smooth cell decomposition and defines the exponential ... More
On Whitney embedding of o-minimal manifoldsApr 10 2019We prove a definable version of the Whitney embedding theorem for abstract-definable $\mathcal{C}^p$ manifolds with $1\leq p<\infty$, namely: every abstract-definable $\mathcal{C}^p$ manifold is abstract-definable $C^p$ embedded into $R^N$, for some positive ... More
Homogeneous length functions on Groups: Intertwined computer & human proofsApr 10 2019We describe a case of an interplay between human and computer proving which played a role in the discovery of an interesting mathematical result. The unusual feature of the use of computers here was that a computer generated but human readable proof was ... More
On the automorphism group of the universal homogeneous meet-treeApr 10 2019We show that the countable universal homogeneous meet-tree has a generic automorphism, but it does not have a generic pair of automorphisms.
On the automorphism group of the universal homogeneous meet-treeApr 10 2019Apr 16 2019We show that the countable universal homogeneous meet-tree has a generic automorphism, but it does not have a generic pair of automorphisms.
The Complexity of Definability by Open First-Order FormulasApr 09 2019In this article we formally define and investigate the computational complexity of the Definability Problem for open first-order formulas (i.e., quantifier free first-order formulas) with equality. Given a logic $\mathbf{\mathcal{L}}$, the $\mathbf{\mathcal{L}}$-Definability ... More
Derivatives of normal functions in reverse mathematicsApr 09 2019Consider a normal function $f$ on the ordinals (i. e. a function $f$ that is strictly increasing and continuous at limit stages). By enumerating the fixed points of $f$ we obtain a faster normal function $f'$, called the derivative of $f$. The present ... More
Higher random indestructibility of MAD familiesApr 09 2019We give a combinatorial characterization of when a maximal almost disjoint family of a weakly compact cardinal $\kappa$ is indestructible by the higher random forcing $\mathbb Q_\kappa$. We then use this characterisation to show that $\mathrm{add}(\mathbf{null}_\kappa) ... More
The Constituents of Sets, Numbers, and Other Mathematical Objects, Part OneApr 09 2019The sets used to construct other mathematical objects are pure sets, which means that all of their elements are sets, which are themselves pure. One set may therefore be within another, not as an element, but as an element of an element, or even deeper, ... More
Learning the undecidable from networked systemsApr 08 2019This article presents a theoretical investigation of computation beyond the Turing barrier from emergent behavior in distributed (or parallel) systems. In particular, we present an algorithmic network that is a mathematical model of a networked population ... More
Kelley-Morse set theory does not prove the class Fodor principleApr 08 2019We show that Kelley-Morse set theory does not prove the class Fodor principle, the assertion that every regressive class function $F:S\to\text{Ord}$ defined on a stationary class $S$ is constant on a stationary subclass. Indeed, it is relatively consistent ... More
Enumeration degrees and non-metrizable topologyApr 08 2019The enumeration degrees of sets of natural numbers can be identified with the degrees of difficulty of enumerating neighborhood bases of points in a universal second-countable $T_0$-space (e.g. the $\omega$-power of the Sierpi\'nski space). Hence, every ... More
A General Framework for the Semantics of Type TheoryApr 08 2019We propose an abstract notion of a type theory to unify the semantics of various type theories including Martin-L\"{o}f type theory, two-level type theory and cubical type theory. We establish basic results in the semantics of type theory: every type ... More
Unilateral weighted shifts on $\ell^2$Apr 08 2019Given a unilateral shift $B_w$ (determined by a bounded sequence $w$), a sequence $x \in \ell^2$ is "hypercyclic" for $w$ iff the forward iterates of $x$ under $B_w$ are dense in $\ell^2$. We show that it is possible to make the set of $x \in \ell^2$ ... More
The complexity of 3-colouring $H$-colourable graphsApr 05 2019We study the complexity of approximation on satisfiable instances for graph homomorphism problems. For a fixed graph $H$, the $H$-colouring problem is to decide whether a given graph has a homomorphism to $H$. By a result of Hell and Ne\v{s}et\v{r}il, ... More
Automating Resolution is NP-HardApr 05 2019We show that the problem of finding a Resolution refutation that is at most polynomially longer than a shortest one is NP-hard. In the parlance of proof complexity, Resolution is not automatizable unless P = NP. Indeed, we show it is NP-hard to distinguish ... More
Conceptual proofs of the Menger and Rothberger gamesApr 04 2019We provide conceptual proofs of the two most fundamental theorems concerning topological games and open covers: Hurewicz's Theorem concerning the Menger game, and Pawlikowski's Theorem concerning the Rothberger game.
Controlling cardinal characteristics without adding realsApr 04 2019We investigate the behavior of cardinal characteristics of the reals under extensions that do not add new ${<}\kappa$-sequences (for some regular $\kappa$). As an application, we present models (assuming the consistency of three strongly compact cardinals) ... More
A small ultrafilter number at smaller cardinalsApr 04 2019It is proved to be consistent relative to a measurable cardinal that there is a uniform ultrafilter on the real numbers which is generated by fewer than the maximum possible number of sets. It is also shown to be consistent relative to a supercompact ... More
On supercompactness of $ω_1$Apr 03 2019This paper studies structural consequences of supercompactness of $\omega_1$ under $\sf{ZF}$. We show that the Axiom of Dependent Choice $(\sf{DC})$ follows from "$\omega_1$ is supercompact". "$\omega_1$ is supercompact" also implies that $\sf{AD}^+$, ... More
Expanding Polynomials and Pairs of Polynomials in Characteristic 0Apr 03 2019We begin a generalized study of sum-product type phenomenon in different fields by considering pairs $P(x,y)$ and $Q(x,y)$ of two variable polynomials that simultaneously exhibit small symmetric expansion. Our first result is that such $P(x,y)$ and $Q(x,y)$ ... More
Inversion, Iteration, and the Art of Dual WieldingApr 02 2019The humble $\dagger$ ("dagger") is used to denote two different operations in category theory: Taking the adjoint of a morphism (in dagger categories) and finding the least fixed point of a functional (in categories enriched in domains). While these two ... More
The strength of compactness for countable complete linear ordersApr 02 2019We investigate the statement "the order topology of every countable complete linear order is compact" in the framework of reverse mathematics, and we find that the statement's strength depends on the precise formulation of compactness. If we require that ... More
New relations and separations of conjectures about incompleteness in the fnite domainApr 02 2019Our main results are in the following three sections: 1. We prove new relations between proof complexity conjectures that are discussed in \cite{pu18}. 2. We investigate the existence of p-optimal proof systems for $\mathsf{TAUT}$, assuming the collapse ... More
New relations and separations of conjectures about incompleteness in the finite domainApr 02 2019Apr 05 2019Our main results are in the following three sections: 1. We prove new relations between proof complexity conjectures that are discussed in \cite{pu18}. 2. We investigate the existence of p-optimal proof systems for $\mathsf{TAUT}$, assuming the collapse ... More
Temporal Landscapes: A Graphical Temporal Logic for ReasoningApr 01 2019We present an elementary introduction to a new logic for reasoning about behaviors that occur over time. This logic is based on temporal type theory. The syntax of the logic is similar to the usual first-order logic; what differs is the notion of truth ... More
Hardy fields, the intermediate value property, and $ω$-freenessApr 01 2019We discuss the conjecture that every maximal Hardy field has the Intermediate Value Property for differential polynomials, and its equivalence to the statement that all maximal Hardy field are elementarily equivalent to the differential field of transseries. ... More
Choiceless Löwenheim-Skolem property and uniform definability of groundsApr 01 2019In this paper, without the axiom of choice, we show that if some downward L\"owenheim-Skolem property holds then all grounds are uniformly definable. We also prove that the axiom of choice is forceable if and only if the universe is a small extension ... More
Antichains of Copies of Ultrahomogeneous StructuresApr 01 2019We investigate possible cardinalities of maximal antichains in the poset of copies $\langle \mathbb P(\mathbb X),\subset \rangle$ of a countable ultrahomogeneous relational structure $\mathbb X$. It turns out that if the age of $\mathbb X$ has the strong ... More
Aristotelian assertoric syllogisticMar 31 2019Aristotelian assertoric syllogistic, which is currently of growing interest, has attracted the attention of the founders of modern logic, who approached it in several (semantical and syntactical) ways. Further approaches were introduced later on. These ... More
Notes on the tightness of $G_δ$-modificationsMar 31 2019We construct a countably tight normal $T_1$ space $X$ with $t(X_\delta) >2^\omega$. This is an answer to the question posed by Dow-Juh\'asz-Soukup-Szentmikl\'ossy-Weiss. We also show that if the continuum is not so large, then the tightness of $G_\delta$-modifications ... More
Groups definable in Presburger arithmeticMar 31 2019We determine all groups definable in Presburger arithmetic, up to a finite index subgroup.
$σ$-Continuous functions and related cardinal characteristics of the continuumMar 30 2019Apr 02 2019A function $f:X\to Y$ between topological spaces is called $\sigma$-$continuous$ (resp. $\bar\sigma$-$continuous$) if there exists a (closed) cover $\{X_n\}_{n\in\omega}$ of $X$ such that for every $n\in\omega$ the restriction $f{\restriction}X_n$ is ... More
Borel sets of Rado graphs and Ramsey's TheoremMar 30 2019The well-known Galvin-Prikry Theorem states that Borel subsets of the Baire space are Ramsey: Given any Borel subset $\mathcal{X}\subseteq [\omega]^{\omega}$, where $[\omega]^{\omega}$ is endowed with the metric topology, each infinite subset $X\subseteq ... More
Martin's Maximum and the Diagonal Reflection PrincipleMar 30 2019Apr 03 2019We prove that Martin's Maximum does not imply the Diagonal Reflection Principle for stationary subsets of $[ \omega_2 ]^\omega$.
A note on "Another ordering of the ten cardinal characteristics in Cichoń's Diagram" and further remarksMar 30 2019In this note, we relax the hypothesis of the main results in Kellner-Shelah-T\v{a}nasie's "Another ordering of the ten cardinal characteristics in Cicho\'n's diagram".
Modelling informational entropyMar 29 2019By 'informational entropy', we understand an inherent boundary to knowability, due e.g. to perceptual, theoretical, evidential or linguistic limits. In this paper, we discuss a logical framework in which this boundary is incorporated into the semantic ... More
The precontraction group of the field of logarithmic transseries $\mathbb{T}_{\log}$Mar 28 2019As a first step to understand the theory of the structure $\mathbb{T}_{\log}$ of logarithmic transseries as an ordered valued logarithmic field, we focus on the map $\chi$ induced by the logarithm of $\mathbb{T}_{\log}$ in its value group $\Gamma_{\log}$ ... More
Towards the undecidability of atomicity for permutation classes via the undecidability of joint embedding for hereditary graph classesMar 28 2019We work towards answering a question of Ru\v{s}kuc on the decidability of atomicity for permutation classes, which is equivalent to the decidability of the joint embedding property when permutations are viewed as structures in a language of two linear ... More
Sequent calculi and interpolation for non-normal logicsMar 27 2019G3-style Sequent calculi for the logics in the cube of non-normal modal logics and for their deontic extensions are introduced. For each of the calculi considered, we prove that weakening and contraction are height-preserving admissible, and we give a ... More
Sequent calculi and interpolation for non-normal logicsMar 27 2019Apr 01 2019G3-style Sequent calculi for the logics in the cube of non-normal modal logics and for their deontic extensions are introduced. For each of the calculi considered, we prove that weakening and contraction are height-preserving admissible, and we give a ... More
Partial results on dp-finite fieldsMar 27 2019We prove that NIP valued fields of positive characteristic are henselian. Furthermore, we partially generalize the known results on dp-minimal fields to dp-finite fields. We prove a dichotomy: if K is a sufficiently saturated dp-finite expansion of a ... More
A Logic of Objective and Subjective Oughts (full paper with proofs)Mar 25 2019The relation between agentive action, knowledge, and obligation is central to the understanding of responsibility --a main topic in Artificial Intelligence. Based on the view that an appropriate formalization of said relation would contribute to the development ... More
Guessing models imply the singular cardinal hypothesisMar 25 2019In this article we prove three main theorems: (1) guessing models are internally unbounded, (2) for any regular cardinal $\kappa \ge \omega_2$, $\textsf{ISP}(\kappa)$ implies that $\textsf{SCH}$ holds above $\kappa$, and (3) forcing posets which have ... More
Infinite forcing and the generic multiverseMar 24 2019In this article we present a technique for selecting models of set theory that are complete in a model-theoretic sense. Specifically, we will apply Robinson infinite forcing to the collections of models of ZFC obtained by Cohen forcing. This technique ... More
Degree spectra for transcendence in fieldsMar 23 2019We show that for both the unary relation of transcendence and the finitary relation of algebraic independence on a field, the degree spectra of these relations may consist of any single computably enumerable Turing degree, or of those c.e. degrees above ... More
The number of models of a fixed Scott rank, for a counterexample to the analytic Vaught conjectureMar 23 2019We show that if $\gamma \in \omega \cup \{\aleph_{0}\}$ and $\mathcal{A}$ is a counterexample to the analytic Vaught conjecture having exactly $\gamma$ many models of Scott rank $\omega_{1}$, then there exists a club $C \subseteq \omega_{1}$ such that ... More
On extensions of partial isometriesMar 22 2019In this paper we define a notion of S-extension for a metric space and study minimality and coherence of S-extensions. We give a complete characterization of all finite minimal S-extensions of a given finite metric space. We also define a notion of ultraextensive ... More
Effective Aspects of Bernoulli RandomnessMar 22 2019In this paper, we study Bernoulli random sequences, i.e., sequences that are Martin-L\"of random with respect to a Bernoulli measure $\mu_p$ for some $p\in[0,1]$, where we allow for the possibility that $p$ is noncomputable. We focus in particular on ... More
Rule-Based Translation of Application-Level QoS Constraints into SDN Configurations for the IoTMar 22 2019In this paper, we propose an approach for the automated translation of application-level requirements regarding the logical workflow and its QoS into a configuration of the underlying network substrate. Our goal is to facilitate the integration of QoS ... More
A Note on OTM-Realizability and Constructive Set TheoriesMar 21 2019We define an ordinalized version of Kleene's realizability interpretation of intuitionistic logic by replacing Turing machines with Koepke's ordinal Turing machines (OTMs), thus obtaining a notion of realizability applying to arbitrary statements in the ... More
Multi-adjoint concept lattices via quantaloid-enriched categoriesMar 21 2019With quantaloids carefully constructed from multi-adjoint frames, it is shown that multi-adjoint concept lattices, multi-adjoint property-oriented concept lattices and multi-adjoint object-oriented concept lattices are derivable from Isbell adjunctions, ... More
Coalgebraic Geometric LogicMar 21 2019Mar 22 2019Using the theory of coalgebra, we introduce a uniform framework for adding modalities to the language of propositional geometric logic. Models for this logic are based on coalgebras for an endofunctor $\mathsf{T}$ on some full subcategory of the category ... More
Coalgebraic Geometric LogicMar 21 2019Using the theory of coalgebra, we introduce a uniform framework for adding modalities to the language of propositional geometric logic. Models for this logic are based on coalgebras for an endofunctor $\mathsf{T}$ on some full subcategory of the category ... More
Solovay reduction and continuityMar 20 2019The objective of this study is a better understanding of the relationships between reduction and continuity. Solovay reduction is a variation of Turing reduction based on the distance of two real numbers. We characterize Solovay reduction by the existence ... More
Oligomorphic groups are essentially countableMar 20 2019We study the complexity of the isomorphism relation on classes of closed subgroups of $S_\infty$, the group of permutations of the natural numbers. We use the setting of Borel reducibility between equivalence relations on Polish spaces. A closed subgroup ... More
Sets and ProbabilityMar 20 2019In this article the idea of random variables over the set theoretic universe is investigated. We explore what it can mean for a random set to have a specific probability of belonging to an antecedently given class of sets.
Semantic programming: method $Δ_0^p$-enrichments and polynomial computable fixed pointsMar 19 2019Computer programs fast entered in our live and the questions associated with the execution of these programs have become the most relevant in our days. Programs should work efficiently, i.e. work as quickly as possible and spend as little resources as ... More
Gauss-Kronecker Curvature and equisingularity at infinity of definable familiesMar 19 2019Assume given a polynomially bounded o-minimal structure expanding the real numbers. Let $(T_s)_{s\in \mathbb{R}}$ be a globally definable one parameter family of $C^2$-hypersurfaces of $\mathbb{R}^n$. Upon defining the notion of generalized critical value ... More
Uncountable structures are not classifiable up to bi-embeddabilityMar 18 2019Answering some of the main questions from [MR13], we show that whenever $\kappa$ is a cardinal satisfying $\kappa^{< \kappa} = \kappa > \omega$, then the embeddability relation between $\kappa$-sized structures is strongly invariantly universal, and hence ... More
An ultrapower construction of the multiplier algebra of a C*-algebraMar 18 2019Using ultrapowers of C*-algebras we provide a new construction of the multiplier algebra of a C*-algebra. This extends the work of Avsec and Goldbring in the article "Boundary amenability of groups via ultrapowers" to the setting of noncommutative and ... More
Mekler's construction and tree propertiesMar 17 2019Mekler constructed a way to produce a pure group from any given structure where the construction preserves $\kappa$-stability for any cardinal $\kappa$. Not only the stability, it is known that his construction preserves various model-theoretic properties ... More
The Destruction of the Axiom of Determinacy by Forcings on $\mathbb{R}$ when $Θ$ is RegularMar 16 2019$\mathsf{ZF + AD}$ proves that for all nontrivial forcings $\mathbb{P}$ on a wellorderable set of cardinality less than $\Theta$, $1_{\mathbb{P}} \Vdash_{\mathbb{P}} \neg\mathsf{AD}$. $\mathsf{ZF + AD} + \Theta$ is regular proves that for all nontrivial ... More
Coding in graphs and linear orderingsMar 16 2019There is a Turing computable embedding $\Phi$ of directed graphs $A$ in undirected graphs. Moreover, there is a fixed tuple of formulas that give a uniform interpretation; i.e., for all directed graphs $A$, these formulas interpret $A$ in $\Phi(G)$. It ... More
Multi-topological semantics for intuitionistic modal logicMar 16 2019We present three examples of \textit{multi-topological} semantics for intuitionistic modal logic with one modal operator $\Box$ (which behaves in some sense like necessity). We show that it is possible to treat neighborhood models, introduced earlier, ... More
Uniform rationality of Poincaré series of p-adic equivalence relations and Igusa's conjecture on exponential sumsMar 15 2019This thesis contains some new results on the uniform rationality of Poincar\'e series of p-adic equivalence relations and Igusa's conjecture on exponential sums
Dp-minimal expansions of discrete ordered abelian groupsMar 14 2019If $\mathscr{Z}$ is a dp-minimal expansion of a discrete ordered abelian group $(Z,<,+)$ and $\mathscr{Z}$ does not admit a nontrivial definable convex subgroup then $\mathscr{Z}$ is interdefinable with $(Z,<,+)$ and $(Z,<,+)$ is elementarily equivalent ... More
Mutual CoinductionMar 14 2019Mar 21 2019In this paper we present mutual coinduction as a dual of mutual induction and also as a generalization of standard coinduction. In particular, we present a precise formal definition of mutual induction and mutual coinduction. In the process we present ... More
Mutual CoinductionMar 14 2019Mar 19 2019In this paper we present mutual coinduction as a dual of mutual induction and as a generalization of standard coinduction. In particular, we present a formal definition of mutual induction and mutual coinduction, and in the process we present, and prove, ... More
Mutual CoinductionMar 14 2019In this paper we present mutual coinduction as a dual of mutual induction and as a generalization of standard coinduction. In particular, we present a formal definition of mutual induction and mutual coinduction, and in the process we present, and prove, ... More
Mutual CoinductionMar 14 2019Apr 08 2019In this paper we present mutual coinduction as a dual of mutual induction and also as a generalization of standard coinduction. In particular, we present a precise formal definition of mutual induction and mutual coinduction. In the process we present ... More
Combinatorial Principles and some questions concerning L-like properties and DC$_κ$Mar 14 2019We extend a result of Arthur Apter which answer a question of Matthew Foreman and Menachem Magidor related to mutually stationary sets. We also extend a result of Arthur Apter which answer a question of W. Hugh Woodin and prove a conjecture by Ioanna ... More
A two-dimensional metric temporal logicMar 14 2019We introduce a two-dimensional metric (interval) temporal logic whose internal and external time flows are dense linear orderings. We provide a suitable semantics and a sequent calculus with axioms for equality and extralogical axioms. Then we prove completeness ... More
Elementary subgroups of the free group are free factors - a new proofMar 14 2019In this note we give a new proof of the fact that an elementary subgroup (in the sense of first-order theory) of a non abelian free group $\mathbb{F}$ must be a free factor. The proof is based on definability of orbits of elements of under automorphisms ... More
Equivalents of the finitary non-deterministic inductive definitionsMar 14 2019We present statements equivalent to some fragments of the principle of non-deterministic inductive definitions (NID) by van den Berg (2013), working in a weak subsystem of constructive set theory CZF. We show that several statements in constructive topology ... More