The stable regularity lemma revisited
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- by Maryanthe Malliaris and Anand Pillay
- Proc. Amer. Math. Soc. 144 (2016), 1761-1765
- DOI: https://doi.org/10.1090/proc/12870
- Published electronically: September 9, 2015
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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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Bibliographic Information
- Maryanthe Malliaris
- Affiliation: Department of Mathematics, University of Chicago, 5734 University Avenue, Chicago, Illinois 60637
- MR Author ID: 864805
- Email: mem@math.uchicago.edu
- Anand Pillay
- Affiliation: Department of Mathematics, University of Notre Dame, Notre Dame, Indiana 46556
- MR Author ID: 139610
- Email: apilla@nd.edu
- Received by editor(s): May 1, 2015
- Published electronically: September 9, 2015
- Additional Notes: The first author was partially supported by NSF grant DMS-1300634 and a Sloan fellowship
The second author was partially supported by NSF grant DMS-1360702 - Communicated by: Mirna Džamonja
- © Copyright 2015 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 144 (2016), 1761-1765
- MSC (2010): Primary 03C45, 03C98, 05C75
- DOI: https://doi.org/10.1090/proc/12870
- MathSciNet review: 3451251