## Abstract

We prove the following instance of a conjecture stated in [P. E. Eleftheriou and Y. Peterzil, Definable quotients of locally definable groups, Selecta Math. (N.S.) 18(4) (2012) 885-903]. Let G be an abelian semialgebraic group over a real closed field R and let X be a semialgebraic subset of G. Then the group generated by X contains a generic set and, if connected, it is divisible. More generally, the same result holds when X is definable in any o-minimal expansion of R which is elementarily equivalent to a an,exp. We observe that the above statement is equivalent to saying: there exists an m such that ςi=1m(X - X) is an approximate subgroup of G.

Original language | English |
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Article number | 2 |

Pages (from-to) | 2050009:1-2050009:17 |

Number of pages | 17 |

Journal | Journal of Mathematical Logic |

Volume | 20 |

Issue number | 2 |

DOIs | |

State | Published - 1 Aug 2020 |

### Bibliographical note

DBLP License: DBLP's bibliographic metadata records provided through http://dblp.org/ are distributed under a Creative Commons CC0 1.0 Universal Public Domain Dedication. Although the bibliographic metadata records are provided consistent with CC0 1.0 Dedication, the content described by the metadata records is not. Content may be subject to copyright, rights of privacy, rights of publicity and other restrictions.## Keywords

- Semialgebraic groups
- approximate groups
- generic sets
- lattices
- locally definable groups

## ASJC Scopus subject areas

- Logic