Monadic stability and growth rates of ω-categorical structures. 



Abstract: We will present the following work by Samuel Braunfeld. 

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 exponentiel. This allow us to confirm some longstanding conjectures of Macpherson proving the existence of gaps not previously recognized.