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