O-minimal cohomology: finiteness and invariance results

Details O-minimal cohomology: finiteness and invariance results O-minimal cohomology: finiteness and invariance results

2007-05-23

arxiv.org/abs/0705.3425v2

Journal of Mathematical Logic (JML), Volume 9, Issue 2(2009), pp. 167-182

Mathematics

Logic

28 pages, 7 figures and diagrams Added the hypothesis that singletons are construcible to section 3. Corrected misprints

Scientific paper

10.1142/S0219061309000859

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.

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