相关论文: Extending the Language of Set Theory

Axiomatizing mathematical structures is a goal of Mathematical Logic. Axiomatizability of the theories of some structures have turned out to be quite difficult and challenging, and some remain open. However axiomatization of some…

We define a logic of propositional formula schemata adding to the syntax of propositional logic indexed propositions and iterated connectives ranging over intervals parameterized by arithmetic variables. The satisfiability problem is shown…

The use of exponentials in linear logic greatly enhances its expressive power. In this paper we focus on nonassociative noncommutative multiplicative linear logic, and systematically explore modal axioms K, T, and 4 as well as the…

We contribute to the knowledge of the quantifier completions and their applications by using the language of doctrines. This algebraic presentation allows us to properly analyse the behaviour of the existential and universal quantifiers. We…

Finite group theorists have established many formulas that express interesting properties of a finite group in terms of sums of characters of the group. An obstacle to applying these formulas is lack of control over the dimensions of…

Real-valued logics underlie an increasing number of neuro-symbolic approaches, though typically their logical inference capabilities are characterized only qualitatively. We provide foundations for establishing the correctness and power of…

We introduced a new continued fraction expansions in our previous paper. For these expansions, we show formulae of probability about incomplete quotients. Furthermore, we prove the existence of invariant measures with respect to the…

We study languages over infinite alphabets equipped with some structure that can be tested by recognizing automata. We develop a framework for studying such alphabets and the ensuing automata theory, where the key role is played by an…

We investigate the position that foundational theories should be modelled on ordinary computability. In this context, we investigate the metamathematics of $\Sigma$ formulas. We consider theories whose axioms are implications between…

Questions of set-theoretic size play an essential role in category theory, especially the distinction between sets and proper classes (or small sets and large sets). There are many different ways to formalize this, and which choice is made…

In this paper, we give a purely cohomological interpretation of the extension problem for (super) Lie algebras; that is the problem of extending a Lie algebra by another Lie algebra. We then give a similar interpretation of infinitesimal…

We introduced the notation of a set of prohibitions and give definitions of a complete set and a crucial word with respect to a given set of prohibitions. We consider 3 particular sets which appear in different areas of mathematics and for…

We consider an extension of linear-time temporal logic (LTL) with both local and remote data constraints interpreted over a concrete domain. This extension is a natural extension of constraint LTL and the Temporal Logic of Repeating Values,…

We prove completeness, interpolation and omitting types for certain predicate topological logics that properly extend the first order case. We aslo count the non isomorphic topological models of a countable theory

A few notes about infinite trees in a descriptive set-theoretic setting.

This lecture notes are intended for the students taking courses in mathematical control theory. They are concerned with the attainability problem with constraints. The exposition is oriented to the linear control problems with the impulse…

This article discusses the logical errors in the liar paradox, G\"odel's incompleteness theorems, Russell's paradox, and the halting problem. In order to avoid these errors, a redefinition of logic has been presented, which is concluded as…

We study links between first-order formulas and arbitrary properties for families of theories, classes of structures and their isomorphism types. Possibilities for ranks and degrees for formulas and theories with respect to given properties…

Given a structure $M$ we introduce infinitary logic expansions, which generalise the Morleyisation. We show that these expansions are tame, in the sense that they preserve and reflect both the Embedding Ramsey Property (ERP) and the…

The article proposes a new technique for proving the undefinability of logical connectives through each other and illustrates the technique with several examples. Some of the obtained results are new proofs of the existing theorems, others…