Choice-Free Duality for Tarski Algebras

IF 0.5 4区数学 Q3 MATHEMATICS

Applied Categorical Structures Pub Date : 2025-06-25 DOI:10.1007/s10485-025-09816-0

Sergio Arturo Celani, Luciano Javier González

引用次数: 0

Abstract

In [N. Bezhanishvili and W. H. Holliday. Choice-free Stone duality. J. Symb. Log., 85(1):109–148, 2020.], the authors develop a choice-free topological duality for the algebraic category of Boolean algebras. We adapt the techniques and constructions given by Bezhanishvili and Holliday to develop a topological duality for the algebraic category of Tarski algebras without using the Axiom of Choice. Then, we show that the duality presented here for Tarski algebras is in fact a generalization of the duality given by Bezhanishvili and Holliday for Boolean algebras. We also obtain a choice-free topological duality for the algebraic category of generalized Boolean algebra.

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Tarski代数的无选择对偶性

在[N。Bezhanishvili和W. H. Holliday。无选择石的二元性。j . Symb。日志。中国生物医学工程学报，28(1):389 - 398,2020。]，作者为布尔代数的代数范畴开发了一个无选择拓扑对偶。我们采用Bezhanishvili和Holliday给出的技术和构造，在不使用选择公理的情况下，发展了Tarski代数范畴的拓扑对偶性。然后，我们证明了这里给出的Tarski代数的对偶性实际上是Bezhanishvili和Holliday给出的布尔代数对偶性的推广。对于广义布尔代数的代数范畴，我们也得到了一个无选择拓扑对偶。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Applied Categorical Structures 数学-数学

CiteScore

1.30

自引率

16.70%

发文量

审稿时长

>12 weeks

期刊介绍： Applied Categorical Structures focuses on applications of results, techniques and ideas from category theory to mathematics, physics and computer science. These include the study of topological and algebraic categories, representation theory, algebraic geometry, homological and homotopical algebra, derived and triangulated categories, categorification of (geometric) invariants, categorical investigations in mathematical physics, higher category theory and applications, categorical investigations in functional analysis, in continuous order theory and in theoretical computer science. In addition, the journal also follows the development of emerging fields in which the application of categorical methods proves to be relevant. Applied Categorical Structures publishes both carefully refereed research papers and survey papers. It promotes communication and increases the dissemination of new results and ideas among mathematicians and computer scientists who use categorical methods in their research.