Groups definable in ordered vector spaces over ordered division rings

Type of Publication: Journal article
Publication status: Published
Author: Eleftheriou, Pantelis E.; Starchenko, Sergei
Year of publication: 2014
Published in: Journal of Symbolic Logic ; 72 (2014), 4. - pp. 1108-1140. - Cambridge University Press. - ISSN 0022-4812. - eISSN 1943-5886
DOI (citable link): https://dx.doi.org/10.2178/jsl/1203350776
Summary:
Let M = 〈M, +, <, 0, {λ}λЄDλЄD〉 be an ordered vector space over an ordered division ring D, and G = 〈G, ⊕, eG〉 an n-dimensional group definable in M. We show that if G is definably compact and definably connected with respect to the t-topology, then it is definably isomorphic to a ‘definable quotient group’ U/L, for some convex V-definable subgroup U of 〈Mn, +〉 and a lattice L of rank n. As two consequences, we derive Pillay's conjecture for a saturated M as above and we show that the o-minimal fundamental group of G is isomorphic to L.
Subject (DDC): 510 Mathematics
Refereed: Yes

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ELEFTHERIOU, Pantelis E., Sergei STARCHENKO, 2014. Groups definable in ordered vector spaces over ordered division rings. In: Journal of Symbolic Logic. Cambridge University Press. 72(4), pp. 1108-1140. ISSN 0022-4812. eISSN 1943-5886. Available under: doi: 10.2178/jsl/1203350776

@article{Eleftheriou2014-03-12Group-49487, title={Groups definable in ordered vector spaces over ordered division rings}, year={2014}, doi={10.2178/jsl/1203350776}, number={4}, volume={72}, issn={0022-4812}, journal={Journal of Symbolic Logic}, pages={1108--1140}, author={Eleftheriou, Pantelis E. and Starchenko, Sergei} }

2020-05-13T18:02:39Z Groups definable in ordered vector spaces over ordered division rings Starchenko, Sergei terms-of-use Eleftheriou, Pantelis E. 2014-03-12 Let M = 〈M, +, <, 0, {λ}<sub>λЄD</sub>λЄD〉 be an ordered vector space over an ordered division ring D, and G = 〈G, ⊕, e<sub>G</sub>〉 an n-dimensional group definable in M. We show that if G is definably compact and definably connected with respect to the t-topology, then it is definably isomorphic to a ‘definable quotient group’ U/L, for some convex V-definable subgroup U of 〈M<sup>n</sup>, +〉 and a lattice L of rank n. As two consequences, we derive Pillay's conjecture for a saturated M as above and we show that the o-minimal fundamental group of G is isomorphic to L. 2020-05-13T18:02:39Z Eleftheriou, Pantelis E. Starchenko, Sergei eng

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