Research Training Network in Model Theory
Publications > Preprint server > Preprint Number 1499

Preprint Number 1499

Previous Next Preprint server

1499. Pierre Simon
On omega-categorical structures with few finite substructures

Submission date: 15 October 2018


We establish new results on the possible growth rates for the sequence (f_n) counting the number of orbits of a given oligomorphic group on unordered sets of size n. Macpherson showed that for primitive actions, the growth is at least exponential (if the sequence is not constant equal to 1). The best lower bound previously known for the base of the exponential was obtained by Merola. We establishing the optimal value of 2 in the case where the structure is unstable. This allows us to improve on Merola's bound and also obtain the optimal value for structures homogeneous in a finite relational language. Finally, we show that the study of sequences (f_n) of sub-exponential growth reduces to the omega-stable case.

Mathematics Subject Classification: 03C15, 03C68, 05A16, 20B27

Keywords and phrases:

Full text arXiv 1810.06531: pdf, ps.

Last updated: March 23 2021 10:20 Please send your corrections to: