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Permutation groups on countable vector spaces over prime fields

Logic 2021-12-13 v1 Group Theory

Abstract

We describe all closed permutation groups which act on the set of vectors of a countable vector space VV over a prime field of odd order and which contain all automorphisms of VV. In particular, we prove that their number is finite. These groups correspond, up to first-order interdefinability, precisely to all structures with a first-order definition in VV.

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Cite

@article{arxiv.2112.05229,
  title  = {Permutation groups on countable vector spaces over prime fields},
  author = {Bertalan Bodor and Michael Pinsker and Lyra Schiffer and Csaba Szabó},
  journal= {arXiv preprint arXiv:2112.05229},
  year   = {2021}
}

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29 pages