塔斯基关于选择的定理与NFU的可选公理推广

Q2 Arts and Humanities

Bulletin of the Section of Logic Pub Date : 2023-09-28 DOI:10.18778/0138-0680.2023.25

Tin Adlešić, Vedran Čačić

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引用次数: 0

摘要

本文用无穷公理和选择公理(NFU+Inf+AC)扩充了带原子的Quine新基础中类型级有序对的存在性。该证明使用了Tarski的选择定理，即NFU+Inf+AC定理。因此，我们有理由提出NFU的一个新的公理扩展，以便几乎从一开始就获得类型级有序对。这个公理化就是NFU+Inf+AC+Tarski，是NFU+Inf+AC的保守推广。

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Tarski's theorem about choice and the alternative axiomatic extension of NFU

In this paper we rigorously prove the existence of type-level ordered pairs in Quine's New Foundations with atoms, augmented by the axiom of infinity and the axiom of choice (NFU+Inf+AC). The proof uses Tarski's theorem about choice, which is a theorem of NFU+Inf+AC. Therefore, we have a justification for proposing a new axiomatic extension of NFU, in order to obtain type-level ordered pairs almost from the beginning. This axiomatization is NFU+Inf+AC+Tarski, a conservative extension of NFU+Inf+AC.

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来源期刊

Bulletin of the Section of Logic Arts and Humanities-Philosophy

CiteScore

0.90

自引率

0.00%

发文量

审稿时长

8 weeks