Journal of Symbolic Logic

A definability result for compact complex spaces

Dale Radin

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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(y). We show that the set Ak,d:={y∈ Y: the number of d-dimensional components of Xy is <k} is analytically constructible, i.e., is a definable set when X and Y are compact complex spaces and f: X→ Y is a holomorphic map. The analogous result in the context of algebraic geometry gives rise to the definability of Morley degree.

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J. Symbolic Logic, Volume 69, Issue 1 (2004), 241-254.

First available in Project Euclid: 2 April 2004

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Radin, Dale. A definability result for compact complex spaces. J. Symbolic Logic 69 (2004), no. 1, 241--254. doi:10.2178/jsl/1080938839.

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