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A definability result for compact complex spaces

Published online by Cambridge University Press:  12 March 2014

Dale Radin
Dale Radin*
Affiliation:
Department of Mathematics, University of Illinois at Chicago, Chicago, IL, 60607, USA, E-mail: radind@math.uic.edu
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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 x 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

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.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 69 , Issue 1 , March 2004 , pp. 241 - 254
Copyright
Copyright © Association for Symbolic Logic 2004

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References

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