Continuous stable regularity
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2021
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| _version_ | 1866912075549245440 |
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| author | Chavarria, Nicolas Conant, Gabriel Pillay, Anand |
| author_facet | Chavarria, Nicolas Conant, Gabriel Pillay, Anand |
| contents | 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 Keisler measures for stable continuous formulas. Along the way, we develop some basic tools around ultraproducts of metric structures and linear functionals on continuous formulas, and we also describe several concrete families of examples of stable functions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2111_05435 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Continuous stable regularity Chavarria, Nicolas Conant, Gabriel Pillay, Anand Logic Combinatorics 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 Keisler measures for stable continuous formulas. Along the way, we develop some basic tools around ultraproducts of metric structures and linear functionals on continuous formulas, and we also describe several concrete families of examples of stable functions. |
| title | Continuous stable regularity |
| topic | Logic Combinatorics |
| url | https://arxiv.org/abs/2111.05435 |