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Groups definable in ordered vector spaces over ordered division rings

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2014

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Starchenko, Sergei

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https://doi.org/10.2178/jsl/1203350776
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Journal of Symbolic Logic. Cambridge University Press. 2014, 72(4), pp. 1108-1140. ISSN 0022-4812. eISSN 1943-5886. Available under: doi: 10.2178/jsl/1203350776

Zusammenfassung

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.

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510 Mathematik

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ISO 690ELEFTHERIOU, Pantelis E., Sergei STARCHENKO, 2014. Groups definable in ordered vector spaces over ordered division rings. In: Journal of Symbolic Logic. Cambridge University Press. 2014, 72(4), pp. 1108-1140. ISSN 0022-4812. eISSN 1943-5886. Available under: doi: 10.2178/jsl/1203350776
BibTex
@article{Eleftheriou2014-03-12Group-49487,
  year={2014},
  doi={10.2178/jsl/1203350776},
  title={Groups definable in ordered vector spaces over ordered division rings},
  number={4},
  volume={72},
  issn={0022-4812},
  journal={Journal of Symbolic Logic},
  pages={1108--1140},
  author={Eleftheriou, Pantelis E. and Starchenko, Sergei}
}
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