A note on the non-existence of prime models of theories of pseudo-finite fields

2020/04/12 by Zoé Chatzidakis, Chatzidakis, Zoé
Computer Science · Mathematics · #03C50 #03C60 #12L12 #Advanced Topology and Set Theory #Computability, Logic, AI Algorithms #FOS: Mathematics #Logic (math.LO) #Mathematical and Theoretical Analysis #Secondary 12E20

paper · pdf · doi:10.48550/arxiv.2004.05593

openalex publication_date 2020/04/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show that if a field A is not pseudo-finite, then there is no prime model of the theory of pseudo-finite fields over A. Assuming GCH, we generalise this result to κ-prime models, for κa regular uncountable cardinal or ℵ_ε.

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