The stable regularity lemma revisited
Logic
2016-04-18 v2 Combinatorics
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.
Cite
@article{arxiv.1504.06288,
title = {The stable regularity lemma revisited},
author = {Maryanthe Malliaris and Anand Pillay},
journal= {arXiv preprint arXiv:1504.06288},
year = {2016}
}
Comments
6 pages. This second version takes into account some comments of Sergei Starchenko that additional cases need to be handled in the proof of Lemma 2.1