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Non-standard lattices and o-minimal groups

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2013

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https://doi.org/10.2178/bsl.1901020
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The Bulletin of Symbolic Logic. Association for Symbolic Logic. 2013, 19(1), pp. 56-76. ISSN 1079-8986. eISSN 1943-5894. Available under: doi: 10.2178/bsl.1901020

Zusammenfassung

We describe a recent program from the study of definable groups in certain o-minimal structures. A central notion of this program is that of a (geometric) lattice. We propose a definition of a lattice in an arbitrary first-order structure. We then use it to describe, uniformly, various structure theorems for o-minimal groups, each time recovering a lattice that captures some significant invariant of the group at hand. The analysis first goes through a local level, where a pertinent notion of pregeometry and generic elements is each time introduced.

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510 Mathematik

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ISO 690ELEFTHERIOU, Pantelis E., 2013. Non-standard lattices and o-minimal groups. In: The Bulletin of Symbolic Logic. Association for Symbolic Logic. 2013, 19(1), pp. 56-76. ISSN 1079-8986. eISSN 1943-5894. Available under: doi: 10.2178/bsl.1901020
BibTex
@article{Eleftheriou2013Nonst-49647,
  year={2013},
  doi={10.2178/bsl.1901020},
  title={Non-standard lattices and o-minimal groups},
  url={https://www.jstor.org/stable/41825306},
  number={1},
  volume={19},
  issn={1079-8986},
  journal={The Bulletin of Symbolic Logic},
  pages={56--76},
  author={Eleftheriou, Pantelis E.}
}
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    <dcterms:abstract xml:lang="eng">We describe a recent program from the study of definable groups in certain o-minimal structures. A central notion of this program is that of a (geometric) lattice. We propose a definition of a lattice in an arbitrary first-order structure. We then use it to describe, uniformly, various structure theorems for o-minimal groups, each time recovering a lattice that captures some significant invariant of the group at hand. The analysis first goes through a local level, where a pertinent notion of pregeometry and generic elements is each time introduced.</dcterms:abstract>
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URL der Originalveröffentl.
https://www.jstor.org/stable/41825306

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2020-05-26

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