The theory of hereditarily bounded sets

IF 0.4 4区数学 Q4 LOGIC

Mathematical Logic Quarterly Pub Date : 2022-04-03 DOI:10.1002/malq.202100020

Emil Jeřábek

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引用次数: 1

Abstract

We show that for any $k \in ω$ , the structure $⟨ H_{k}, \in ⟩$ of sets that are hereditarily of size at most k is decidable. We provide a transparent complete axiomatization of its theory, a quantifier elimination result, and tight bounds on its computational complexity. This stands in stark contrast to the structure $V_{ω} = ⋃_{k} H_{k}$ of hereditarily finite sets, which is well known to be bi-interpretable with the standard model of arithmetic $⟨ N, +, \cdot ⟩$ .

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遗传有界集理论

我们证明对于任何k∈ω $k\in \omega$，遗传上大小最多为k的集合的结构⟨H k，∈⟩$\langle H_k,{\in }\rangle$是可决定的。我们提供了它的理论的一个透明的完全公理化，一个量词消除结果，以及它的计算复杂性的严格界限。这与遗传有限集的结构V ω = k H k $V_\omega =\bigcup _kH_k$形成鲜明对比，这是众所周知的，用算术⟨N， +，·⟩$\langle \mathbb {N},+,\cdot \rangle$的标准模型是双可解释的。

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

Mathematical Logic Quarterly 数学-数学

CiteScore

0.60

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Mathematical Logic Quarterly publishes original contributions on mathematical logic and foundations of mathematics and related areas, such as general logic, model theory, recursion theory, set theory, proof theory and constructive mathematics, algebraic logic, nonstandard models, and logical aspects of theoretical computer science.