Labelled growth rates of $\omega$-categorical structures and applications in choiceless set theory

Bertalan Bodor, Samuel Braunfeld, James E. Hanson

We study the labelled growth rate of an $\omega$-categorical structure $\mathfrak{A}$, i.e., the number of orbits of $Aut(\mathfrak{A})$ on $n$-tuples of distinct elements, and show tha…