Submission date: 18 November 2014.

Abstract:

We observe that the nonstandard finite cardinality of a definable set in a strongly minimal pseudofinite structure D is a polynomial over the integers in the nonstandard finite cardinality of D. We conclude that D is unimodular, hence also locally modular. We also deduce a regularity lemma for graphs definable in strongly minimal pseudofinite structures. The paper is elementary, and the only surprising thing about it is that the results were not explicitly noted before.

Mathematics Subject Classification: 03C45, 05C75

Keywords and phrases:

Full text arXiv 1411.5008: pdf, ps.