O-极小上同调：有限性和不变性结果
O-minimal cohomology: finiteness and invariance results
摘要：
本文证明了群的o-极小扩张上的可定义紧集的上同调群在语言的初等扩张和扩张下是非线性生成的和不变的。在o-极小结构扩张域的附加假设下，我们还研究了可定义的可定义紧集的可定义减族的交的上同调。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
