有据局部有限图中有限集理论的独立性结果

Pub Date : 2024-02-16 DOI:10.1007/s11225-023-10087-w

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引用次数: 0

摘要

摘要我们考虑了与有限集合论（即不含无穷公理的 Zermelo-Fraenkel 集合论）子集相对应的所有组合上可能的系统，并为其中的每一个系统提供了一个作为该理论模型的基础良好的局部有限图，或者证明这是不可能的。为此，我们开发了图的公理闭包技术。

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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Independence Results for Finite Set Theories in Well-Founded Locally Finite Graphs

Abstract

We consider all combinatorially possible systems corresponding to subsets of finite set theory (i.e., Zermelo-Fraenkel set theory without the axiom of infinity) and for each of them either provide a well-founded locally finite graph that is a model of that theory or show that this is impossible. To that end, we develop the technique of axiom closure of graphs.

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