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| Main Author: | |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2508.00511 |
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Table of 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.