Nondefinability of Rings of Integers in Most Algebraic Fields

Philip Dittmann; Arno Fehm

doi:10.1215/00294527-2021-0029

August 2021 Nondefinability of Rings of Integers in Most Algebraic Fields

Philip Dittmann, Arno Fehm

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Abstract

We show that the set of algebraic extensions F of $\mathbb{Q}$ in which $\mathbb{Z}$ or the ring of integers ${\mathcal{O}_{F}}$ are definable is meager in the set of all algebraic extensions.

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Philip Dittmann and Arno Fehm "Nondefinability of Rings of Integers in Most Algebraic Fields," Notre Dame Journal of Formal Logic 62(3), 589-592, (August 2021). https://doi.org/10.1215/00294527-2021-0029

Received: 30 December 2020; Accepted: 25 May 2021; Published: August 2021

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