- journal article metadata
European Mathematical Society Publishing House
2016-09-19 17:05:07
Journal of the European Mathematical Society
J. Eur. Math. Soc.
JEMS
1435-9855
1435-9863
General
10.4171/JEMS
http://www.ems-ph.org/doi/10.4171/JEMS
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European Mathematical Society Publishing House
Zuerich, Switzerland
© European Mathematical Society
13
2011
4
On NIP and invariant measures
Ehud
Hrushovski
Hebrew University, JERUSALEM, ISRAEL
Anand
Pillay
University of Leeds, LEEDS, UNITED KINGDOM
We study forking, Lascar strong types, Keisler measures and definable groups, under an assumption of $NIP$ (not the independence property), continuing aspects of the paper \cite{NIP}. Among key results are (i) if $p = tp(b/A)$ does not fork over $A$ then the Lascar strong type of $b$ over $A$ coincides with the compact strong type of $b$ over $A$ and any global nonforking extension of $p$ is Borel definable over $bdd(A)$, (ii) analogous statements for Keisler measures and definable groups, including the fact that $G^{000} = G^{00}$ for $G$ definably amenable, (iii) definitions, characterizations and properties of “generically stable" types and groups, (iv) uniqueness of invariant (under the group action) Keisler measures on groups with finitely satisfiable generics, (v) a proof of the compact domination conjecture for (definably compact) commutative groups in $o$-minimal expansions of real closed fields.
Field theory and polynomials
Group theory and generalizations
General
1005
1061
10.4171/JEMS/274
http://www.ems-ph.org/doi/10.4171/JEMS/274