Monadic stability and growth rates of ω$\omega$‐categorical structures

Autor:	Samuel Braunfeld
Rok vydání:	2022
Předmět:	General Mathematics Mathematics - Combinatorics 03C15 05A16 20B27 Mathematics - Logic Mathematics - Group Theory
Zdroj:	Proceedings of the London Mathematical Society. 124:373-386
ISSN:	1460-244X 0024-6115
DOI:	10.1112/plms.12429
Popis:	For $M$ $\omega$-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 Cameron and Macpherson and proving the existence of gaps not previously recognized. Comment: 13 pages; to appear in Proceedings of the London Mathematical Society
Databáze:	OpenAIRE
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