简单类型理论中的数学结构

IF 0.6 3区数学 Q2 LOGIC

Studia Logica Pub Date : 2024-07-23 DOI:10.1007/s11225-024-10133-1

Samuel González-Castillo

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引用次数: 0

摘要

我们提出了简单类型理论的扩展，它包含了任何类型的数学结构（任何顺序）的类型。为此，我们正式定义了两个结构同构的含义。我们在 NFU 集合论中为这两种扩展建模，以证明它们的相对一致性。

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Mathematical Structures Within Simple Type Theory

We present an extension of simple type theory that incorporates types for any kind of mathematical structure (of any order). We further extend this system allowing isomorphic structures to be identified within these types thanks to some syntactical restrictions; for this purpose, we formally define what it means for two structures to be isomorphic. We model both extensions in NFU set theory in order to prove their relative consistency.

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来源期刊

Studia Logica MATHEMATICS-LOGIC

CiteScore

1.70

自引率

14.30%

发文量

审稿时长

6-12 weeks

期刊介绍： The leading idea of Lvov-Warsaw School of Logic, Philosophy and Mathematics was to investigate philosophical problems by means of rigorous methods of mathematics. Evidence of the great success the School experienced is the fact that it has become generally recognized as Polish Style Logic. Today Polish Style Logic is no longer exclusively a Polish speciality. It is represented by numerous logicians, mathematicians and philosophers from research centers all over the world.