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ASSOCIATIVITY OF THE MORLEY PRODUCT OF INVARIANT MEASURES IN NIP THEORIES

Published online by Cambridge University Press:  12 August 2021

GABRIEL CONANT
Affiliation:
DPMMS, UNIVERSITY OF CAMBRIDGECAMBRIDGE CB3 0WB, UKE-mail:[email protected]
KYLE GANNON
Affiliation:
DEPARTMENT OF MATHEMATICS UNIVERSITY OF CALIFORNIA, LOS ANGELES LOS ANGELES, CA90095, USAE-mail:[email protected]

Abstract

In light of a gap found by Krupiński, we give a new proof of associativity for the Morley (or “nonforking”) product of invariant measures in NIP theories.

Type
Article
Copyright
© Association for Symbolic Logic 2021

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References

REFERENCES

Conant, G. and Gannon, K., Remarks on generic stability in independent theories . Annals of Pure and Applied Logic , vol. 171 (2020), no. 2, p. 102736, 20.10.1016/j.apal.2019.102736CrossRefGoogle Scholar
Conant, G., Gannon, K. and Hanson, J., Keisler measures in the wild, preprint, 2021, arXiv2103.09137.Google Scholar
Hrushovski, E. and Pillay, A., On NIP and invariant measures . Journal of European Mathematical Society (JEMS) , vol. 13 (2011), no. 4, pp. 10051061.10.4171/JEMS/274CrossRefGoogle Scholar
Hrushovski, E., Pillay, A., and Simon, P., Generically stable and smooth measures in NIP theories. Transactions of American Mathematical Society, vol. 365 (2013), no. 5, pp. 23412366.10.1090/S0002-9947-2012-05626-1CrossRefGoogle Scholar
Keisler, H.J., Measures and forking . Annals of Pure and Applied Logic , vol. 34 (1987), no. 2, pp. 119169.10.1016/0168-0072(87)90069-8CrossRefGoogle Scholar
Simon, P., A Guide to NIP Theories , Lecture Notes in Logic, vol. 44, Cambridge University Press, Cambridge, 2015.10.1017/CBO9781107415133CrossRefGoogle Scholar
Starchenko, S., NIP, Keisler measures and combinatorics, no. 390, 2017, Séminaire Bourbaki. Vol. 2015/2016. Exposés 1104–1119, pp. Exp. No. 1114, 303–334.Google Scholar