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arXiv · 2009.08967

Complete type amalgamation for non-standard finite groups

Amador Martin-Pizarro·Daniel Palacín
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Abstract

We extend previous work on Hrushovski's stabilizer's theorem and prove a measure-theoretic 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.

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Amador Martin-Pizarro, Daniel Palacín. 2020-09-18. Complete type amalgamation for non-standard finite groups. https://doi.org/10.2140/mt.2024.3.1

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