Journal of Symbolic Logic

The {L}aczkovich—{K}omjáth property for coanalytic equivalence relations

Su Gao, Steve Jackson, and Vincent Kieftenbeld

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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 ∈ K An meets uncountably many E-equivalence classes for every K ∈ [ω]ω, then there exists a K ∈ [ω]ω such that ⋂n ∈ K An contains a perfect set of pairwise E-inequivalent elements.

Article information

Source
J. Symbolic Logic, Volume 75, Issue 3 (2010), 1091-1101.

Dates
First available in Project Euclid: 9 July 2010

Permanent link to this document
https://projecteuclid.org/euclid.jsl/1278682218

Digital Object Identifier
doi:10.2178/jsl/1278682218

Mathematical Reviews number (MathSciNet)
MR2723785

Zentralblatt MATH identifier
1227.03065

Subjects
Primary: 03E15: Descriptive set theory [See also 28A05, 54H05] 54H05: Descriptive set theory (topological aspects of Borel, analytic, projective, etc. sets) [See also 03E15, 26A21, 28A05]
Secondary: 28A05: Classes of sets (Borel fields, $\sigma$-rings, etc.), measurable sets, Suslin sets, analytic sets [See also 03E15, 26A21, 54H05]

Keywords
Limit superior of a sequence of sets coanalytic equivalence relations Laczkovich—Komjáth property

Citation

Gao, Su; Jackson, Steve; Kieftenbeld, Vincent. The {L}aczkovich—{K}omjáth property for coanalytic equivalence relations. J. Symbolic Logic 75 (2010), no. 3, 1091--1101. doi:10.2178/jsl/1278682218. https://projecteuclid.org/euclid.jsl/1278682218


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