MODNET
Research Training Network in Model Theory
Publications > Preprint server > Preprint Number 1719

Preprint Number 1719

Previous Next Preprint server


1719. Pantelis E. Eleftheriou
Groups definable in weakly o-minimal non-valuational structures
E-mail:

Submission date: 22 January 2020

Abstract:

Let M be a weakly o-minimal non-valuational structure, and N its canonical o-minimal extension (by Wencel). We prove that every group G definable in \mathcal M is a subgroup of a group K definable in N, which is canonical in the sense that it is the smallest such group. As an application, we obtain that G^{00}= G ∩ K^{00}, and establish Pillay's Conjecture in this setting: G/G^{00}, equipped with the logic topology, is a compact Lie group, and if G has finitely satisfiable generics, then dim_{Lie}(G/G^{00})= dim(G).

Mathematics Subject Classification: 03C60, 03C64

Keywords and phrases:

Full text arXiv 2001.08209: pdf, ps.


Last updated: February 7 2020 13:09 Please send your corrections to: