On the regularity of almost stable relations
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866913969594171392 |
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| author | Girón, Marcos |
| author_facet | Girón, Marcos |
| contents | We develop a general theory of local stability up to belonging to an ideal (e.g. having measure zero). From a model-theoretic perspective, we prove a stationarity principle for almost stable formulas in this sense, and build a topological space of partial types whose Cantor-Bendixson rank is finite. The interaction of this space with Keisler measures and definable groups yields, on the one hand, a regularity lemma for infinite graphs where the edge relation is almost stable, and, on the other hand, the existence of definable stabilizer subgroups. As an application, we prove a finite graph regularity lemma and an arithmetic regularity lemma for almost stable relations in arbitrary finite groups. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_00511 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the regularity of almost stable relations Girón, Marcos Logic We develop a general theory of local stability up to belonging to an ideal (e.g. having measure zero). From a model-theoretic perspective, we prove a stationarity principle for almost stable formulas in this sense, and build a topological space of partial types whose Cantor-Bendixson rank is finite. The interaction of this space with Keisler measures and definable groups yields, on the one hand, a regularity lemma for infinite graphs where the edge relation is almost stable, and, on the other hand, the existence of definable stabilizer subgroups. As an application, we prove a finite graph regularity lemma and an arithmetic regularity lemma for almost stable relations in arbitrary finite groups. |
| title | On the regularity of almost stable relations |
| topic | Logic |
| url | https://arxiv.org/abs/2508.00511 |