The Laczkovich-Komjath 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 (A_n) a sequence of analytic subsets of X. We prove that if limsup_K A_n meets uncountably many E-equivalence classes for every K in [ω]^ω, then there exists a K in [ω]^ω such that ∩_K A_n contains a perfect set of pairwise E-inequivalent elements.

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Table of Contents

1. Introduction

2. Coding and sets

3. Canonical cofinal sequences

4. A completely good pair

5. Proof of the main theorem

           References

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