The stable regularity lemma revisited

Malliaris, Maryanthe; Pillay, Anand

doi:10.1090/proc/12870

The stable regularity lemma revisited
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by Maryanthe Malliaris and Anand Pillay PDF

Proc. Amer. Math. Soc. 144 (2016), 1761-1765 Request permission

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 ${\bar M}$ and the formula $R(x,y)$ is stable. The proof is rather quick, making use of local stability theory. The special case where $(V,W,R)$ is pseudofinite, $\mu$, $\nu$ are the counting measures, and ${\bar M}$ is suitably chosen (for example a nonstandard model of set theory), yields the stable regularity theorem of a work by the first author and S. Shelah, though without explicit bounds or equitability.

References

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