Let L be a countable language. We say that a countable infinite L-structure M admits an invariant measure when there is a probability measure on the space of L-structures with the same underlying set… (More)

Building on recent results regarding symmetric probabilistic constructions of countable structures, we provide a method for constructing probability measures, concentrated on certain classes of… (More)

We consider the space of countable structures with fixed underlying set in a given countable language. We show that the number of ergodic probability measures on this space that are S∞-invariant and… (More)

Let L be a countable language. We characterize, in terms of definable closure, those countable theories Σ of Lω1,ω(L) for which there exists an S∞-invariant probability measure on the collection of… (More)

We study ergodic Sym(N)-invariant probability measures on the space of L-structures with domain N. We call such measures “ergodic structures”. In particular, we are interested in the properly ergodic… (More)

We generalize the stable graph regularity lemma of Malliaris and Shelah to the case of finite structures in finite relational languages, e.g., finite hypergraphs. We show that under the… (More)