Publications > Preprint server > Preprint Number 2696
Preprint Number 2696
2696. Samuel Braunfeld, Colin Jahel, Paolo Marimon When invariance implies exchangeability (and applications to invariant Keisler measures) E-mail: Submission date: 15 August 2024 Abstract:
We study the problem of when, given a homogeneous structure M and a space
S of expansions of M, every Aut(M)-invariant probability measure
on S is exchangeable (i.e. S_∞-invariant). We define a condition of
k-overlap closedness on M which implies exchangeability of random
expansions by a class of structures whose finite substructures are all
contained in a hereditary class with labelled growth-rate O(e^{n^{k+δ}})
for all δ>0. For example, the generic tetrahedron-free 3-hypergraph is
2-overlap closed and so all of its random expansions by graphs are
exchangeable. Our more general results on k-overlap closedness for
homogeneous structures imply the same for every finitely bounded homogeneous
3-hypergraph with free amalgamation. Our results extend and recover both the
work of Angel, Kechris and Lyons on invariant random orderings of homogeneous
structures and some of the work of Crane and Towsner, and Ackerman on
relatively exchangeable structures. We also study conditions under which there
are non-exchangeable invariant random expansions looking at the universal
homogeneous kay-graphs. Mathematics Subject Classification: 0C315, 0C345, 60G09, 60C05, 37A05 Keywords and phrases: |
Last updated: August 23 2024 14:13 | Please send your corrections to: |