Extensions of Solovay's system S without independent sets of axioms

IF 0.6 2区数学 Q2 LOGIC Annals of Pure and Applied Logic Pub Date : 2023-09-01 DOI:10.1016/j.apal.2023.103360

Igor Gorbunov , Dmitry Shkatov

引用次数: 0

Abstract

Chagrov and Zakharyaschev posed the problem of existence of extensions of Solovay's system S, which is a non-normalizable quasi-normal modal logic, that do not admit deductively independent sets of axioms. This paper gives a solution by exhibiting countably many extensions of S without deductively independent sets of axioms.

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没有独立公理集的Solovay系统s的扩张

Chagrov和Zakharyaschev提出了Solovay系统S的扩展的存在性问题，Solovay系统S是一个不可归一化的拟正态模态逻辑，它不允许演绎独立的公理集。本文给出了一个解，给出了无演绎独立公理集的S的可数扩展。

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

Annals of Pure and Applied Logic 数学-数学

CiteScore

1.40

自引率

12.50%

发文量

审稿时长

200 days

期刊介绍： The journal Annals of Pure and Applied Logic publishes high quality papers in all areas of mathematical logic as well as applications of logic in mathematics, in theoretical computer science and in other related disciplines. All submissions to the journal should be mathematically correct, well written (preferably in English)and contain relevant new results that are of significant interest to a substantial number of logicians. The journal also considers submissions that are somewhat too long to be published by other journals while being too short to form a separate memoir provided that they are of particular outstanding quality and broad interest. In addition, Annals of Pure and Applied Logic occasionally publishes special issues of selected papers from well-chosen conferences in pure and applied logic.

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