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arXiv:1807.07102 [math.LO]AbstractReferencesReviewsResources

NIP omega-categorical structures: the rank 1 case

Pierre Simon

Published 2018-07-18Version 1

We classify primitive, rank 1, omega-categorical structures having polynomially many types over finite sets, or equivalently at most exponential growth of the number of finite substructures. For a fixed number of 4-types, we show that there are only finitely many such structures and that all are built out of finitely many linear orders interacting in a restricted number of ways. As an example of application, we deduce the classification of primitive structures homogeneous in a language consisting of n linear orders as well as all reducts of such structures.

Comments: 52 pages
Categories: math.LO, math.CO
Subjects: 03C15, 03C64, 03C68, 06A05
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