25 citations · 70 across the 21 of their papers we have counts for
37 papers
Generically stable Keisler measures
Gabriel Conant, Kyle Gannon, James E. Hanson
Given a first-order theory (in discrete or continuous logic) and a Borel-definable global Keisler measure in , we show that the following conditions are equivalent: $(i)…
Encoding orders and trees in real-valued functions
G Conant, C Terry
We prove function-theoretic analogues of a quantitative result of Hodges on extracting the order property from a sufficiently large 2-tree coded in a binary relation. Similar analo…
VC-dimension of generalized progressions in some nonabelian groups
Gabriel Conant, Aycin Iplikci Arodirik, Tora Ozawa +1
We analyze generalized progressions in some nonabelian groups using a measure of complexity called VC-dimension, which was originally introduced in statistical learning theory by V…
An analytic version of stable arithmetic regularity
Gabriel Conant, Anand Pillay
We prove a structure theorem for stable functions on amenable groups, which extends the arithmetic regularity lemma for stable subsets of finite groups. Given a group , a functi…
Three surprising instances of dividing
Gabriel Conant, Alex Kruckman
We give three counterexamples to the folklore claim that in an arbitrary theory, if a complete type over a set does not divide over , then no extension of …
Generic stability, randomizations, and NIP formulas
Gabriel Conant, Kyle Gannon, James E. Hanson
We prove a number of results relating the concepts of Keisler measures, generic stability, randomizations, and NIP formulas. Among other things, we do the following: (1) We introdu…
Pseudofinite proofs of the stable graph regularity lemma
G. Conant, C. Terry
This expository article is based on two lectures given by the first author at the Fields Institute in the Fall 2021 Thematic Program on Trends in Pure and Applied Model Theory. We…
Compactifications of pseudofinite and pseudo-amenable groups
Gabriel Conant, Ehud Hrushovski, Anand Pillay
We first give simplified and corrected accounts of some results in \cite{PiRCP} on compactifications of pseudofinite groups. For instance, we use a classical theorem of Turing \cit…
Higher arity stability and the functional order property
A. Abd-Aldaim, G. Conant, C. Terry
The -dimensional functional order property () is a combinatorial property of a -partitioned formula. This notion arose in work of Terry and Wolf, which iden…
Enriching a predicate and tame expansions of the integers
Gabriel Conant, Christian d'Elbée, Yatir Halevi +2
Given a structure and a stably embedded -definable set , we prove tameness preservation results when enriching the induced structure on by some furt…
Continuous stable regularity
Nicolas Chavarria, Gabriel Conant, Anand Pillay
We prove an analytic version of the stable graph regularity lemma from \cite{MaSh}, which applies to stable functions . Our methods involve continuous m…
Separation for isometric group actions and hyperimaginary independence
Gabriel Conant, James Hanson
We generalize P. M. Neumann's Lemma to the setting of isometric actions on metric spaces and use it to prove several results in continuous logic related to algebraic independence.…
Associativity of the Morley product of invariant measures in NIP theories
Gabriel Conant, Kyle Gannon
In light of a gap found by Krupiński, we give a new proof of associativity for the Morley (or "nonforking") product of invariant measures in NIP theories.
Keisler measures in the wild
Gabriel Conant, Kyle Gannon, James Hanson
We investigate Keisler measures in arbitrary theories. Our initial focus is on Borel definability. We show that when working over countable parameter sets in countable theories, Bo…
Approximate subgroups with bounded VC-dimension
Gabriel Conant, Anand Pillay
We combine the fundamental results of Breuillard, Green, and Tao on the structure of approximate groups, together with "tame" arithmetic regularity methods based on work of the aut…
Quantitative structure of stable sets in arbitrary finite groups
Gabriel Conant
We show that a -stable set in a finite group can be approximated, up to given error , by left cosets of a subgroup of index . This improves the bound in…
Remarks on generic stability in independent theories
Gabriel Conant, Kyle Gannon
In NIP theories, generically stable Keisler measures can be characterized in several ways. We analyze these various forms of "generic stability" in arbitrary theories. Among other…
Stability in a group
Gabriel Conant
We develop local stable group theory directly from topological dynamics, and extend the main results in this subject to the setting of stability "in a model". Specifically, given a…
Weakly minimal groups with a new predicate
Gabriel Conant, Michael C. Laskowski
Fix a weakly minimal (i.e., superstable -rank ) structure . Let be an expansion by constants for an elementary substructure, and let be an ar…
On finite sets of small tripling or small alternation in arbitrary groups
Gabriel Conant
We prove Bogolyubov-Ruzsa-type results for finite subsets of groups with small tripling, , or small alternation, . As applications,…
Structure and regularity for subsets of groups with finite VC-dimension
G. Conant, A. Pillay, C. Terry
Suppose is a finite group and is such that has VC-dimension strictly less than . We find algebraically well-structured sets in which, up t…
Pseudofinite groups and VC-dimension
Gabriel Conant, Anand Pillay
We develop local NIP group theory in the context of pseudofinite groups. In particular, given a sufficiently saturated pseudofinite structure expanding a group, and left invari…
A group version of stable regularity
G. Conant, A. Pillay, C. Terry
We prove that, given and , there is an integer such that the following holds. Suppose is a finite group and is -stable. Then there is a nor…
Independence in generic incidence structures
Gabriel Conant, Alex Kruckman
We study the theory of existentially closed incidence structures omitting the complete incidence structure , which can also be viewed as existentially closed $K_…