Structure theorems for o-minimal expansions of groups

Mario J. Edmundo
2000 Annals of Pure and Applied Logic  
Let Rbe an o-minimal expanion of an ordered group (R, 0, 1, +, <) with distinguished positive element 1. We first prove that the following are equivalent:(1)R is semi-bounded, (2)R has no poles, (3) R cannot define a real closed field with domain R and order <, (4) R is eventually linear and (5) every R-definable set is a finite union of cones. As a corollary we get that T h(R) has quantifier elimination and universal axiomatization in the language with symbols for the ordered group operations,
more » ... bounded R-definable sets and a symbol for each definable endomorphism of the group (R, 0, +).
doi:10.1016/s0168-0072(99)00043-3 fatcat:z4ynxuexkbcopl5z5eknfvhdj4