Groups definable in linear o-minimal structures: the non-compact case
Pantelis E. Eleftheriou
Source: J. Symbolic Logic Volume 75, Issue 1
(2010), 208-220.
Abstract
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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Permanent link to this document: http://projecteuclid.org/euclid.jsl/1264433916
Digital Object Identifier: doi:10.2178/jsl/1264433916
Zentralblatt MATH identifier: 05681299
Mathematical Reviews number (MathSciNet): MR2605889
References
A. Berarducci, M. Otero, Y. Peterzil, and A. Pillay, A descending chain condition for groups definable in o-minimal structures, Annals of Pure and Applied Logic, vol. 134 (2005), pp. 303--313.
Mathematical Reviews (MathSciNet): MR2139910
Zentralblatt MATH: 1068.03033
Digital Object Identifier: doi:10.1016/j.apal.2005.01.002
N. Bourbaki, Lie groups and Lie algebras. Chapters 1--3, Elements of Mathematics, Springer-Verlag, Berlin, 1989.
Mathematical Reviews (MathSciNet): MR979493
M. Edmundo and P. Eleftheriou, Definable group extensions in semi-bounded o-minimal structures, Mathematical Logic Quarterly, vol. 55 (2009), pp. 598--604.
Mathematical Reviews (MathSciNet): MR2582160
Digital Object Identifier: doi:10.1002/malq.200910027
P. Eleftheriou and S. Starchenko, Groups definable in ordered vector spaces over ordered division rings, Journal of Symbolic Logic, vol. 72 (2007), pp. 1108--1140.
Mathematical Reviews (MathSciNet): MR2371195
Zentralblatt MATH: 1130.03028
Digital Object Identifier: doi:10.2178/jsl/1203350776
Project Euclid: euclid.jsl/1203350776
E. Hrushovski, Y. Peterzil, and A. Pillay, Groups, measures, and the NIP, Journal of the American Mathematical Society, vol. 21 (2008), pp. 563--596.
Mathematical Reviews (MathSciNet): MR2373360
Zentralblatt MATH: 1134.03024
Digital Object Identifier: doi:10.1090/S0894-0347-07-00558-9
J. Loveys and Y. Peterzil, Linear o-minimal structures, Israel Journal of Mathematics, vol. 81 (1993), pp. 1--30.
Mathematical Reviews (MathSciNet): MR1231176
Zentralblatt MATH: 0797.03034
Digital Object Identifier: doi:10.1007/BF02761295
A. Onshuus, Groups definable in $\langle \bbQ, +, <\rangle$, Preprint, 2005.
Y. Peterzil and A. Pillay, Generic sets in definably compact groups, Fundamenta Mathematicae, vol. 193 (2007), no. 2, pp. 153--170.
Mathematical Reviews (MathSciNet): MR2282713
Zentralblatt MATH: 1117.03042
Digital Object Identifier: doi:10.4064/fm193-2-4
Y. Peterzil and S. Starchenko, Definable homomorphisms of abelian groups in o-minimal structures, Annals of Pure and Applied Logic, vol. 101 (2000), pp. 1--27.
Mathematical Reviews (MathSciNet): MR1729742
Zentralblatt MATH: 0949.03033
Digital Object Identifier: doi:10.1016/S0168-0072(99)00016-0
Y. Peterzil and C. Steinhorn, Definable compactness and definable subgroups of o-minimal groups, Journal of the London Mathematical Society. Second Series, vol. 69 (1999), pp. 769--786.
Mathematical Reviews (MathSciNet): MR1709079
Zentralblatt MATH: 0935.03047
Digital Object Identifier: doi:10.1112/S0024610799007528
A. Pillay, On groups and fields definable in $o$-minimal structures, Journal of Pure and Applied Algebra, vol. 53 (1988), pp. 239--255.
Mathematical Reviews (MathSciNet): MR961362
Zentralblatt MATH: 0662.03025
Digital Object Identifier: doi:10.1016/0022-4049(88)90125-9
--------, Type-definability, compact Lie groups, and o-minimality, Journal of Mathematical Logic, vol. 4 (2004), pp. 147--162.
Mathematical Reviews (MathSciNet): MR2114965
Zentralblatt MATH: 1069.03029
Digital Object Identifier: doi:10.1142/S0219061304000346
A. Strzebonski, Euler characteristic in semialgebraic and other $\rm o$-minimal groups, Journal of Pure and Applied Algebra, vol. 96 (1994), pp. 173--201.
Mathematical Reviews (MathSciNet): MR1303545
Zentralblatt MATH: 0815.03024
Digital Object Identifier: doi:10.1016/0022-4049(94)90127-9
