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On the regularity of almost stable relations
[Submitted on 1 Aug 2025 (v1), last revised 11 Jun 2026 (this ve · 2026-06-15 · via math updates on arXiv.org

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Abstract: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.

Submission history

From: Marcos Girón [view email]
[v1] Fri, 1 Aug 2025 10:43:41 UTC (30 KB)
[v2] Thu, 11 Jun 2026 20:33:41 UTC (32 KB)

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