没有选择公理的代数补全

IF 0.4 4区数学 Q4 LOGIC

Mathematical Logic Quarterly Pub Date : 2022-07-08 DOI:10.1002/malq.202200001

Jørgen Harmse

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引用次数: 0

摘要

Läuchli和Pincus证明了不能仅从Zermelo-Fraenkel集合论证明所有域的代数补全的存在性。另一方面，重要的特殊情况也会随之而来。特别地，我证明了Q p$ \mathbb {Q}_p$的代数补全可以在Zermelo-Fraenkel集合理论中构造。

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Algebraic completion without the axiom of choice

Läuchli and Pincus showed that existence of algebraic completions of all fields cannot be proved from Zermelo-Fraenkel set theory alone. On the other hand, important special cases do follow. In particular, I show that an algebraic completion of $Q_{p}$ can be constructed in Zermelo-Fraenkel set theory.

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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.