A Definability Result For Compact Complex Spaces

Journal of Symbolic Logic 69 (1):241-254 (2004)
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Abstract

A compact complex space X is viewed as a 1-st order structure by taking predicates for analytic subsets of X, X \times X, … as basic relations. Let f: X→ Y be a proper surjective holomorphic map between complex spaces and set Xy:=f-1. We show that the set Ak,d:={y∈ Y: the number of d-dimensional components of Xy is

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