Research Training Network in Model Theory
Publications > Preprint server > Preprint Number 1933

Preprint Number 1933

Previous Next Preprint server

1933. Alexander Van Abel
Counting in Uncountably Categorical Pseudofinite Structures

Submission date: 4 March 2021


We show that every definable subset of an uncountably categorical pseudofinite structure has pseudofinite cardinality which is polynomial (over the rationals) in the size of any strongly minimal subset, with the degree of the polynomial equal to the Morley rank of the subset. From this fact, we show that classes of finite structures whose ultraproducts all satisfy the same uncountably categorical theory are polynomial $R$-mecs as well as $N$-dimensional asymptotic classes, where $N$ is the Morley rank of the theory.

Mathematics Subject Classification:

Keywords and phrases:

Full text arXiv 2103.03276: pdf, ps.

Last updated: March 23 2021 10:21 Please send your corrections to: