A NOTE ON THE NON-EXISTENCE OF PRIME MODELS OF THEORIES OF PSEUDO-FINITE FIELDS
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 extend this result to $\kappa $ -prime models, for $\kappa $ an uncountable cardinal or $\aleph _\varepsilon $ .
Authors
- Zoé Chatzidakis (ORCID: https://orcid.org/0000-0002-3369-100X)
Institutions
- Sorbonne Paris Cité (FR)
Publication Details
- Journal
- Journal of Symbolic Logic
- Published
- 2025-03-01
- DOI
- https://doi.org/10.1017/jsl.2025.18
- Primary Topic
- Computability, Logic, AI Algorithms
- Type
- article
- Field-Weighted Citation Impact
- 0.00