Related papers: Finite-variable logics do not have weak Beth defin…

The complexity class $NP$ can be logically characterized both through existential second order logic $SO\exists$, as proven by Fagin, and through simulating a Turing machine via the satisfiability problem of propositional logic SAT, as…

It was shown by Visser that Peano Arithmetic has the property that any two bi-interpretable extensions of it (in the same language) are equivalent. Enayat proposed to refer to this property of a theory as tightness and to carry out a more…

SJT reducibility between sets $A,B \subseteq \mathbb N$ is defined by $A \le_{SJT} B$ if for each computable function $h$ that is unbounded and nondecreasing, there is an $h$-bounded uniformly $B$-c.e.\ trace $(T_n)_{n \in \mathbb N} $ such…

Propositional 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…

Let v(n) denote the number of compositions (ordered partitions) of a positive integer n into powers of 2. It appears that the function v(n) satisfies many congruences modulo 2^N. For example, for every integer B there exists (as k tends to…

We study a conjecture by Deaconescu on the solubility of finite groups with claims that if more than half of the elements in a finite group has the same order $k$, then the group is soluble. We show that the original conjecture fails by…

Affine continuous logic is extended to affine integration logic. Affine compactness theorem is proved by both the ultramean construction and Henkin's method. Also, a proof system and a completeness theorem are given. An appropriate variant…

We show that there is a restriction, or modification of the finite-variable fragments of First Order Logic in which a weak form of Craig's Interpolation Theorem holds, but a strong form of this theorem does not hold. Translating these…

We study the two-variable fragments D^2 and IF^2 of dependence logic and independence-friendly logic. We consider the satisfiability and finite satisfiability problems of these logics and show that for D^2, both problems are…

Logic programming, as exemplified by datalog, defines the meaning of a program as its unique smallest model: the deductive closure of its inference rules. However, many problems call for an enumeration of models that vary along some set of…

We prove that for every $\epsilon > 0$ there exists a $\delta > 0$ so that every group of order $n \geq 3$ has at least $\delta \log_{2} n/{(\log_{2} \log_{2} n)}^{3+\epsilon}$ conjugacy classes. This sharpens earlier results of Pyber and…

We present a natural restriction of Hindman's Finite Sums Theorem that admits a simple combinatorial proof (one that does not also prove the full Finite Sums Theorem) and low computability-theoretic and proof-theoretic upper bounds, yet…

In this article we prove results about finite soluble groups that act with fixity 2 or 3.

We consider the extension of two variable logic with quantifiers that state that the number of elements where a formula holds should belong to a given ultimately periodic set. We show that both satisfiability and finite satisfiability of…

This paper presents a study of the finite axiomatizability of transitive logics of finite depth and finite weak width. We prove the finite axiomatizability of each transitive logic of finite depth and of weak width $1$ that is characterized…

The notion of non-deterministic logical matrix (where connectives are interpreted as multi-functions) preserves many good properties of traditional semantics based on logical matrices (where connectives are interpreted as functions) whilst…

We introduce the notion of finitary computable reducibility on equivalence relations on the natural numbers. This is a weakening of the usual notion of computable reducibility, and we show it to be distinct in several ways. In particular,…

We prove general adjoint functor theorems for weakly (co)complete $n$-categories. This class of $n$-categories includes the homotopy $n$-categories of (co)complete $\infty$-categories, so these $n$-categories do not admit all small…

We analyze the periodicity of optimal long products of matrices. A set of matrices is said to have the finiteness property if the maximal rate of growth of long products of matrices taken from the set can be obtained by a periodic product.…

We present a method for proving that a semigroup is finitely based and find some new sufficient conditions under which a monoid is finitely based. As an application, we find a class of finite monoids where the finite basis property behaves…