ZF and its interpretations

IF 0.6 2区数学 Q2 LOGIC

Annals of Pure and Applied Logic Pub Date : 2024-03-04 DOI:10.1016/j.apal.2024.103427

S. Jockwich Martinez , S. Tarafder , G. Venturi

引用次数: 0

Abstract

In this paper, we unify the study of classical and non-classical algebra-valued models of set theory, by studying variations of the interpretation functions for = and ∈. Although, these variations coincide with the standard interpretation in Boolean-valued constructions, nonetheless they extend the scope of validity of $ZF$ to new algebra-valued models. This paper presents, for the first time, non-trivial paraconsistent models of full $ZF$ . Moreover, due to the validity of Leibniz's law in these structures, we will show how to construct proper models of set theory by quotienting these algebra-valued models with respect to equality, modulo the filter of the designated truth-values.

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ZF 及其解释

在本文中，我们通过研究 = 和 ∈ 的解释函数的变化，将集合论的经典和非经典代数值模型的研究统一起来。尽管这些变化与布尔值构造中的标准解释不谋而合，但它们扩展了新的代数值模型的有效性范围。本文首次提出了全......的非三维准一致模型。此外，由于莱布尼兹定律在这些结构中的有效性，我们将展示如何通过对这些代数值模型进行相等的商，模数化指定真值的过滤器，来构造集合论的适当模型。

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.