为学说添加常数和公理

IF 0.4 4区数学 Q4 LOGIC

Mathematical Logic Quarterly Pub Date : 2024-10-08 DOI:10.1002/malq.202300053

Francesca Guffanti

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引用次数: 0

摘要

我们研究了对任何学说来说 "在语言中增加一个常量 "和对主要学说来说 "在理论中增加一个公理 "的意义，说明它们实际上是同一构造的两个实例。我们证明了它们的普遍属性，以及这些构造如何与学说的附加结构相容。为了建立这些构造，我们证明了在有索引的poset的2类中存在着逗点的Kleisli对象。

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Adding a constant and an axiom to a doctrine

We study the meaning of “adding a constant to a language” for any doctrine, and “adding an axiom to a theory” for a primary doctrine, by showing how these are actually two instances of the same construction. We prove their universal properties, and how these constructions are compatible with additional structure on the doctrine. Existence of Kleisli object for comonads in the 2-category of indexed poset is proved in order to build these constructions.

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来源期刊

Mathematical Logic Quarterly 数学-数学

CiteScore

0.60

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Mathematical Logic Quarterly publishes original contributions on mathematical logic and foundations of mathematics and related areas, such as general logic, model theory, recursion theory, set theory, proof theory and constructive mathematics, algebraic logic, nonstandard models, and logical aspects of theoretical computer science.