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Preprint Number 861

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861. Maryanthe Malliaris and Anand Pillay
The stable regularity lemma revisited
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Submission date: 23 April 2015.

Abstract:

We prove a regularity lemma with respect to arbitrary Keisler measures mu on V, nu on W where the bipartite graph (V,W,R) is definable in a saturated structure M and the formula R(x,y) is stable. The proof is rather quick and uses local stability theory. The special case where (V,W,R) is pseudofinite, mu, nu are the counting measures and M is suitably chosen (for example a nonstandard model of set theory), yields the stable regularity theorem of Malliaris-Shelah (Transactions AMS, 366, 2014, 1551-1585), though without explicit bounds or equitability.

Mathematics Subject Classification: 05C75, 03C45, 03C98

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Full text arXiv 1504.06288: pdf, ps.


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