关于域中存在不可判性的两个例子

The Journal of Symbolic Logic Pub Date : 2023-11-23 DOI:10.1017/jsl.2023.87

PHILIP DITTMANN

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引用次数: 0

摘要

我们构造了一个存在上不可判定的完整离散有值混合特征域，它具有存在上可判定的残差域和可判定的代数部分，有力地回答了安斯科姆-费姆提出的一个问题。在此过程中，我们修正了凯萨万-塔纳戈帕尔（Kesavan Thanagopal）的一个构造，构造了一个存在可判的正特征域，它具有存在可判的有限扩展。

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TWO EXAMPLES CONCERNING EXISTENTIAL UNDECIDABILITY IN FIELDS

We construct an existentially undecidable complete discretely valued field of mixed characteristic with existentially decidable residue field and decidable algebraic part, answering a question by Anscombe–Fehm in a strong way. Along the way, we construct an existentially decidable field of positive characteristic with an existentially undecidable finite extension, modifying a construction due to Kesavan Thanagopal.

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The Journal of Symbolic Logic

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