Compact domination for groups definable in linear o-minimal structures
نویسنده
چکیده
منابع مشابه
Groups, measures, and the NIP
We discuss measures, invariant measures on definable groups, and genericity, often in an NIP (failure of the independence property) environment. We complete the proof of the third author’s conjectures relating definably compact groups G in saturated o-minimal structures to compact Lie groups. We also prove some other structural results about such G, for example the existence of a left invariant...
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We prove several structural results on definably compact groups G in o-minimal expansions of real closed fields such as (i) G is definably an almost direct product of a semisimple group and a commutative group, (ii) (G, ·) is elementarily equivalent to (G/G, ·). We also prove results on the internality of finite covers of G in an o-minimal environment, as well as deducing the full compact domin...
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Let M = 〈M, +, <, 0, S〉 be a linear o-minimal expansion of an ordered group, and G = 〈G,⊕, eG〉 an n-dimensional group definable in M. We show that if G is definably connected with respect to the t-topology, then it is definably isomorphic to a definable quotient group U/L, for some convex ∨ definable subgroup U of 〈Mn, +〉 and a lattice L of rank equal to the dimension of the ‘compact part’ of G.
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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 [16]. 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...
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In this note we show: Let R = 〈R, <, +, 0, . . . 〉 be a semi-bounded (respectively, linear) o-minimal expansion of an ordered group, and G a group definable in R of linear dimension m ([Ed1]). Then G is a definable extension of a bounded (respectively, definably compact) definable group B by 〈Rm, +〉.
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ورودعنوان ژورنال:
- Arch. Math. Log.
دوره 48 شماره
صفحات -
تاریخ انتشار 2009