On NIP and invariant measures
| dc.creator | Hrushovski, Ehud | |
| dc.creator | Pillay, Anand | |
| dc.date | 2007-10-11 | |
| dc.date | 2009-01-29 | |
| dc.date.accessioned | 2026-07-07T12:34:59Z | |
| dc.date.available | 2026-07-07T12:34:59Z | |
| dc.description | We study forking, Lascar strong types, Keisler measures and definable groups, under an assumption of $NIP$ (not the independence property), continuing aspects of math.LO/0607442. 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 translation invariant Keisler measures on groups with finitely satisfiable generics (vi) A proof of the compact domination conjecture for definably compact commutative groups in $o$-minimal expansions of real closed fields. | |
| dc.description | Changes from the first version include removing the old section 8 on generic compact domination, giving a more complete account of the Vapnik-Chervonenkis theorem and its applications, the addition of an appendix on the existence of definable Skolem functions in suitable o-minimal structures, as well as expanding and clarifying various proofs | |
| dc.identifier | https://arxiv.org/abs/0710.2330 | |
| dc.identifier | http://arxiv.org/abs/0710.2330 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/217634 | |
| dc.subject | Logic | |
| dc.subject | 03C45, 03C60, 20F67 | |
| dc.title | On NIP and invariant measures | |
| dc.type | text |