On definable Skolem functions and trichotomy

2022/07/22 by Bruno Dinis, Dinis, Bruno, Mário J. Edmundo +1 · 1 citation
Computer Science · Mathematics · #03C64 #Advanced Topology and Set Theory #Computability, Logic, AI Algorithms #FOS: Mathematics #Logic (math.LO) #Rings, Modules, and Algebras

paper · pdf · doi:10.48550/arxiv.2207.11339

openalex publication_date 2022/07/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we give an explicit characterization of o-minimal structures with definable Skolem functions/definable choice. Such structures are, after naming finitely many elements from the prime model, a union of finitely many trivial points each defined over ∅ and finitely many open intervals each a union of a ∅ -definable family of group-intervals with fixed positive elements.

Cited by

• On Definably Compact Semigroups in o-Minimal Structures

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