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Morley degree in unidimensional compact complex spaces. (English) Zbl 1100.03029
Summary: Let \({\mathcal A}\) be the category of all reduced compact complex spaces, viewed as a multi-sorted first-order structure, in the standard way. Let \({\mathcal U}\) be a sub-category of \({\mathcal A}\), which is closed under the taking of products and analytic subsets, and whose morphisms include the projections. Under the assumption that \(\text{Th} ({\mathcal U})\) is unidimensional, we show that Morley rank is equal to Noetherian dimension, in any elementary extension of \({\mathcal U}\). As a result, we are able to show that Morley degree is definable in \(\text{Th}({\mathcal U})\), when \(\text{Th}({\mathcal U})\) is unidimensional.
MSC:
03C65 Models of other mathematical theories
32C15 Complex spaces
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