Non-definability of rings of integers in most algebraic fields

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.

Added some remarks. Accepted for publication in the Notre Dame Journal of Formal Logic

References in corpus (1)

• A topological approach to undefinability in algebraic extensions of $\mathbb{Q}$

Cited by in corpus (2)

• Definability and decidability for rings of integers in totally imaginary fields
• When is the étale open topology a field topology?