A NOTE ON THE NON-EXISTENCE OF PRIME MODELS OF THEORIES OF PSEUDO-FINITE FIELDS
Zoé Chatzidakis · Journal of Symbolic Logic · 2025
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 $ .