O-minimal cohomology: finiteness and invariance results

Abstract

We prove that the cohomology groups of a definably compact set over an o-minimal expansion of a group are finitely generated and invariant under elementary extensions and expansions of the language. We also study the cohomology of the intersection of a definable decreas-ing family of definably compact sets, under the additional assumption that the o-minimal structure expands a field.Comment: 28 pages, 7 figures and diagrams Added the hypothesis that singletons are construcible to section 3. Corrected misprint