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Invariant measures in simple and in small theories

Abstract:
We give examples of (i) a simple theory with a formula (with parameters) which does not fork over ∅ but has 𝜇-measure 0 for every automorphism invariant Keisler measure 𝜇 and (ii) a definable group 𝐺 in a simple theory such that 𝐺 is not definably amenable, i.e. there is no translation invariant Keisler measure on 𝐺. 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.
Publication status:
Published
Peer review status:
Peer reviewed

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Publisher copy:
10.1142/S0219061322500258

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Institution:
University of Oxford
Division:
MPLS
Department:
Mathematical Institute
Oxford college:
Merton College
Role:
Author
ORCID:
0000-0002-2761-6513
Publisher:
World Scientific Publishing
Journal:
Journal of Mathematical Logic More from this journal
Volume:
23
Issue:
2
Article number:
2250025
Publication date:
2022-12-17
Acceptance date:
2022-06-28
DOI:
EISSN:
1793-6691
ISSN:
0219-0613
Language:
English
Keywords:
Pubs id:
1179506
Local pid:
pubs:1179506
Deposit date:
2021-08-01

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