Year: 2024
Type: article
Abstract: We extend previous work on Hrushovski's stabilizer theorem and prove a measuretheoretic version of a well-known result of Pillay-Scanlon-Wagner on products of three types.This generalizes results of Gowers on products of three sets and yields model-theoretic proofs of existing asymptotic results for quasirandom groups.We also obtain a model-theoretic proof of Roth's theorem on the existence of arithmetic progressions of length 3 for subsets of positive density in suitable definably amenable groups, such as countable amenable abelian groups without involutions and ultraproducts of finite abelian groups of odd order.
Source: Model Theory
DOI: 10.2140/mt.2024.3.1
Authors: Amador Martin-Pizarro, Daniel Palacín
Institutions: University of Freiburg, Universidad Complutense de Madrid
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: bronze
Award: G2385450489
OpenAlex ID: W4396517294