没有选择公理的代数补全

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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