相关论文: Finite Representability of Semigroups with Demonic…

This paper presents a sequent calculus and a dual domain semantics for a theory of definite descriptions in which these expressions are formalised in the context of complete sentences by a binary quantifier $I$. $I$ forms a formula from two…

We consider an extension of the unary negation fragment of first-order logic in which arbitrarily many binary symbols may be required to be interpreted as equivalence relations. We show that this extension has the finite model property.…

This note extends some results of a previous paper (math.RT/0403250) about finite dimensional representations of the wreath product symplectic reflection algebra H(k,c,N,G) of rank N attached to a finite subgroup G of SL(2,C) (here k is a…

We show that finite quasisimple groups of Lie type in characteristic $p$ with an irreducible representation of prime degree $r$ over a finite field of characteristic $p$ have orders bounded above by a function of $r$, independent of $p$. We…

Developing an idea of Kapranov and Voevodsky, we introduce a model of weak omega-categories based on directed complexes, combinatorial presentations of pasting diagrams. We propose this as a convenient framework for higher-dimensional…

Training language models to solve complex mathematical problems benefits from curriculum learning progressively training on simpler subproblems. However, existing decomposition methods are often heuristic, offering no guarantees that…

We study atom canonicity for several varieties of cylindric like algebras that contain properly the variety of representable algebras. The algebras in such varieties have relativized representations, and we thereby obtain many omitting…

This paper obtains a completeness result for inequational reasoning with applicative terms without variables in a setting where the intended semantic models are the full structures, the full type hierarchies over preorders for the base…

We study finite first-order satisfiability (FSAT) in the constructive setting of dependent type theory. Employing synthetic accounts of enumerability and decidability, we give a full classification of FSAT depending on the first-order…

We develop a novel formal theory of finite structures, based on a view of finite structures as a fundamental artifact of computing and programming, forming a common platform for computing both within particular finite structures, and in the…

We consider a version of a famous open problem formulated by Kadison, asking whether bounded representations of operator algebras are automatically completely bounded. We investigate this question in the context of amenable operator…

This article explores the model-dependent nature of set cardinality, emphasizing that cardinality is not absolute but varies across different axiomatic frameworks. Although Cantor's diagonal argument shows the real numbers are…

Our goal is to define an algebraic language for reasoning about non-deterministic computations. Towards this goal, we introduce an algebra of string-to-string transductions. Specifically, it is an algebra of partial functions on words over…

We consider deformations of bounded complexes of modules for a profinite group G over a field of positive characteristic. We prove a finiteness theorem which provides some sufficient conditions for the versal deformation of such a complex…

We provide polynomial lower bounds for residual finiteness of residually finite, finitely generated solvable groups that admit infinite order elements in the Fitting subgroup of strict distortion at least exponential. For this class of…

Using a new definition of rank for representations of semisimple groups sharp results are proved for the decay of matrix coefficients of unitary representations of two types of non-split $p$-adic simple algebraic groups of exceptional type.…

This paper investigates the class of finitely presented monoids defined by homogeneous (length-preserving) relations from a computational perspective. The properties of admitting a finite complete rewriting system, having finite derivation…

This paper tackles the problem of synthesizing specifications for nondeterministic programs. For such programs, useful specifications can capture demonic properties, which hold for every nondeterministic execution, but also angelic…

We study isometric representations of product systems of correspondences over the semigroup $\mathbb{N}^k$ which are minimal dilations of finite dimensional, fully coisometric representations. We show the existence of a unique minimal…

First 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…