Year: 2014
Type: preprint
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. In the new version we add a comment on relations to work of Macpherson and Steinhorn, as well as on the limited nature of the examples
Source: arXiv (Cornell University)
Author: Pillay, Anand
Institution: University of Notre Dame
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Funder: National Science Foundation
OpenAlex ID: W2163762340