Groups definable in ordered vector spaces over ordered division rings

Let M = M, +, <, 0, {λ}λ∈D be an ordered vector space over an ordered division ring D, and G = G, ⊕, eG an n-dimensional group definable in M. We show that if G is definably compact and definably connected with respect to t-topology, then it is definably isomorphic to a ‘definable quotient group’ U/L, for some convex -definable subgroup U of Mn, + and a lattice L of rank n. As two consequences, we derive Pillay’s conjecture for M as above and we show that the o-minimal fundamental group of G is isomorphic to L.

• Type: Journal
• Year: 2007
• Where: JSYML
• Authors: Pantelis E. Eleftheriou, Sergei Starchenko
• Keywords: Convex -definable Subgroup, JSYML 2007, Ordered Division, Ordered Vector Space