Complete type amalgamation for non-standard finite groups
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arXiv
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| Format: | Preprint |
| Published: |
2020
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| _version_ | 1866910427455160320 |
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| author | Martin-Pizarro, Amador Palacín, Daniel |
| author_facet | Martin-Pizarro, Amador Palacín, Daniel |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2009_08967 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Complete type amalgamation for non-standard finite groups Martin-Pizarro, Amador Palacín, Daniel Logic Combinatorics 03C45, 11B30 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. |
| title | Complete type amalgamation for non-standard finite groups |
| topic | Logic Combinatorics 03C45, 11B30 |
| url | https://arxiv.org/abs/2009.08967 |