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In this paper we find general criteria to ensure that, in an arbitrary o-minimal structure, the o-minimal cohomology without supports and with definably compact supports of a definable space with coefficients in a sheaf is invariant in elementary extensions and in o-minimal expansions. We also prove the o-minimal analogue of Wilder's finiteness theorem in this context.

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Invariance of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>o</mml:mi></mml:math>-minimal cohomology with definably compact supports

Invariance of o-minimal cohomology with definably compact supports