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math.LO2010
Finding generically stable measures
Pierre Simon
We discuss two constructions for obtaining generically stable Keisler measures in an NIP theory. First, we show how to symmetrize an arbitrary invariant measure to obtain a generic…
math.LO2010
Externally definable sets and dependent pairs
Artem Chernikov, Pierre Simon
We prove that externally definable sets in first order NIP theories have honest definitions, giving a new proof of Shelah's expansion theorem. Also we discuss a weak notion of stab…
math.LO2010
Generically stable and smooth measures in NIP theories
Ehud Hrushovski, Anand Pillay, Pierre Simon
We study stable like behaviour in first order theories without the independence property. We introduce generically stable measures, give characterizatiions, and show their ubiquity…