13 citations · 30 across the 14 of their papers we have counts for
14 papers
Forcing with Invariant Measures
Nathanael Ackerman, Cameron Freer, Mohammad Golshani +2
This paper introduces a model-theoretic generalization of the notion of forcing with random reals, in which forcing gives rise to random generic structures. Specifically, we consid…
Generic sampling and invariant measures on the space of -uniform hypergraphs
Nathanael Ackerman, Cameron Freer, Kyle Gannon +2
We prove a model-theoretic representation theorem for the distribution of an ergodic exchangeable -uniform hypergraph: every such measure arises as the pushforward of the counta…
Big Ramsey Degrees in Ultraproducts of Finite Structures
Dana Bartošová, Mirna Džamonja, Rehana Patel +1
We develop a transfer principle of structural Ramsey theory from finite structures to ultraproducts. We show that under certain mild conditions, when a class of finite structures h…
Fraisse structures with SDAP+, Part II: Simply characterized big Ramsey structures
Rebecca Coulson, Natasha Dobrinen, Rehana Patel
This is Part II of a two-part series regarding Ramsey properties of Fraisse structures satisfying a property called SDAP+, which strengthens the Disjoint Amalgamation Property. In…
Fraisse Structures with SDAP+, Part I: Indivisibility
Rebecca Coulson, Natasha Dobrinen, Rehana Patel
This is Part I of a two-part series regarding Ramsey properties of Fraisse structures satisfying a property called SDAP+, which strengthens the Disjoint Amalgamation Property. We p…
On computable aspects of algebraic and definable closure
Nathanael Ackerman, Cameron Freer, Rehana Patel
We investigate the computability of algebraic closure and definable closure with respect to a collection of formulas. We show that for a computable collection of formulas of quanti…
Fraisse classes with simply characterized big Ramsey degrees
Rebecca Coulson, Natasha Dobrinen, Rehana Patel
We formulate a property strengthening the Disjoint Amalgamation Property and prove that every Fraisse structure in a finite relational language with relation symbols of arity at mo…
The entropy function of an invariant measure
Nathanael Ackerman, Cameron Freer, Rehana Patel
Given a countable relational language , we consider probability measures on the space of -structures with underlying set that are invariant under the logic actio…
Stable regularity for relational structures
Nathanael Ackerman, Cameron Freer, Rehana Patel
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 unde…
Properly ergodic structures
Nathanael Ackerman, Cameron Freer, Alex Kruckman +1
We consider ergodic -invariant probability measures on the space of -structures with domain (for a countable relational language), and…
Countable infinitary theories admitting an invariant measure
Nathanael Ackerman, Cameron Freer, Rehana Patel
Let be a countable language. We characterize, in terms of definable closure, those countable theories of for which there exists an -inva…
A classification of orbits admitting a unique invariant measure
Nathanael Ackerman, Cameron Freer, Aleksandra Kwiatkowska +1
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 ar…
Invariant measures via inverse limits of finite structures
Nathanael Ackerman, Cameron Freer, Jaroslav Nesetril +1
Building on recent results regarding symmetric probabilistic constructions of countable structures, we provide a method for constructing probability measures, concentrated on certa…
Invariant measures concentrated on countable structures
Nathanael Ackerman, Cameron Freer, Rehana Patel
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…