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

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Full text arXiv 2001.08209: pdf, ps.