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Title: Invariant measures in simple and in small theories
We give examples of (i) a simple theory with a formula (with parameters) which does not fork over [Formula: see text] but has [Formula: see text]-measure 0 for every automorphism invariant Keisler measure [Formula: see text] and (ii) a definable group [Formula: see text] in a simple theory such that [Formula: see text] is not definably amenable, i.e. there is no translation invariant Keisler measure on [Formula: see text]. We also discuss paradoxical decompositions both in the setting of discrete groups and of definable groups, and prove some positive results about small theories, including the definable amenability of definable groups.  more » « less
Award ID(s):
1651321
PAR ID:
10441599
Author(s) / Creator(s):
; ; ; ; ; ;
Date Published:
Journal Name:
Journal of Mathematical Logic
Volume:
23
Issue:
02
ISSN:
0219-0613
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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