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The Laczkovich-Komjáth property for coanalytic equivalence relations

Published online by Cambridge University Press:  12 March 2014

Su Gao ,
Steve Jackson  and
Vincent Kieftenbeld
Su Gao
Affiliation:
University of North Texas, Department of Mathematics, 1155 Union Circle #311430, Denton, Tx 76203-5017, USA. E-mail: sgao@unt.edu
Steve Jackson
Affiliation:
University of North Texas, Department of Mathematics, 1155 Union Circle #311430, Denton, Tx 76203-5017, USA. E-mail: jackson@unt.edu
Vincent Kieftenbeld
Affiliation:
University of North Texas, Department of Mathematics, 1155 Union Circle #311430, Denton, Tx 76203-5017, USA. E-mail: kieftenbeld@unt.edu
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Abstract

Let E be a coanalytic equivalence relation on a Polish space X and (An)n∈ω a sequence of analytic subsets of X. We prove that if lim supn∈kAn meets uncountably many E-equivalence classes for every K ∈ [ω]ω, then there exists K ∈ [ω]ω such that ∩n∈kAn contains a perfect set of pairwise E-inequivalent elements.

Keywords

Limit superior of a sequence of setscoanalytic equivalence relationsLaczkovich-Komjáth property
Type
Research Article
Information
The Journal of Symbolic Logic , Volume 75 , Issue 3 , September 2010 , pp. 1091 - 1101
Copyright
Copyright © Association for Symbolic Logic 2010

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References

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