Submission date: 10 October 2019

Abstract:

For M ω-categorical and stable, we investigate the growth rate of M, i.e. the number of orbits of Aut(M) on n-sets, or equivalently the number of n-substructures of M after performing quantifier elimination. We show that monadic stability corresponds to a gap in the spectrum of growth rates, from slower than exponential to faster than exponential. This allows us to give a nearly complete description of the spectrum of slower than exponential growth rates (without the assumption of stability), confirming some longstanding conjectures of Macpherson and reproving some known results.

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

Keywords and phrases:

Full text arXiv 1910.04380: pdf, ps.