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pro vyhledávání: '"Conant, Gabriel"'
Autor:
Conant, Gabriel
We show that if $G$ is an amenable group and $A\subseteq G$ has positive upper Banach density, then there is an identity neighborhood $B$ in the Bohr topology on $G$ that is almost contained in $AA^{-1}$ in the sense that $B\backslash AA^{-1}$ has up
Externí odkaz:
http://arxiv.org/abs/2410.13766
Autor:
Conant, Gabriel, Pillay, Anand
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 $G$, a function $f\colon G\to [-1,1]$ is called stable if the binary function $f(x\
Externí odkaz:
http://arxiv.org/abs/2401.14363
Autor:
Conant, Gabriel, Kruckman, Alex
We give three counterexamples to the folklore claim that in an arbitrary theory, if a complete type $p$ over a set $B$ does not divide over $C\subseteq B$, then no extension of $p$ to a complete type over $\text{acl}(B)$ divides over $C$. Two of our
Externí odkaz:
http://arxiv.org/abs/2311.00609
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 \cite{Turing} to give a simplified proof that any definable compactificati
Externí odkaz:
http://arxiv.org/abs/2308.08440
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 introduce the notion of a Keisler-Morley measure, which plays the role of a M
Externí odkaz:
http://arxiv.org/abs/2308.01801
Given a structure $\mathcal{M}$ and a stably embedded $\emptyset$-definable set $Q$, we prove tameness preservation results when enriching the induced structure on $Q$ by some further structure $\mathcal{Q}$. In particular, we show that if $T=\text{T
Externí odkaz:
http://arxiv.org/abs/2203.07226
Publikováno v:
J. London Math. Soc., 109 (2024)
We prove an analytic version of the stable graph regularity lemma from \cite{MaSh}, which applies to stable functions $f\colon V\times W\to [0,1]$. Our methods involve continuous model theory and, in particular, results on the structure of local Keis
Externí odkaz:
http://arxiv.org/abs/2111.05435
Autor:
Conant, Gabriel, Hanson, James
Publikováno v:
Fundamenta Mathematicae 249 (2022) 97-109
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. In particular, we show that algebraic independence satisfies the full
Externí odkaz:
http://arxiv.org/abs/2110.07763
Autor:
Conant, Gabriel, Gannon, Kyle
Publikováno v:
Journal of Symbolic Logic 86 (2021) no. 3, 1293-1300
In light of a gap found by Krupi\'{n}ski, we give a new proof of associativity for the Morley (or "nonforking") product of invariant measures in NIP theories.
Comment: 7 pages
Comment: 7 pages
Externí odkaz:
http://arxiv.org/abs/2104.08298
Publikováno v:
Model Th. 2 (2023) 1-67
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, Borel definable measures are closed under Morley products and satisfy as
Externí odkaz:
http://arxiv.org/abs/2103.09137