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Homogeneity for open partitions of pairs of reals


Author: Qi Feng
Journal: Trans. Amer. Math. Soc. 339 (1993), 659-684
MSC: Primary 03E05; Secondary 03E15, 03E60
DOI: https://doi.org/10.1090/S0002-9947-1993-1113695-5
MathSciNet review: 1113695
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Abstract: We prove a partition theorem for analytic sets of reals, namely, if $ A \subseteq \mathbb{R}$ is analytic and $ {[A]^2} = {K_0} \cup {K_1}$ with $ {K_0}$ relatively open, then either there is a perfect 0-homogeneous subset or $ A$ is a countable union of $ 1$-homogeneous subsets. We also show that such a partition property for coanalytic sets is the same as that each uncountable coanalytic set contains a perfect subset. A two person game for this partition property is also studied. There are some applications of such partition properties.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1993-1113695-5
Keywords: Homogeneity, open-coloring, games, set theory, descriptive set theory
Article copyright: © Copyright 1993 American Mathematical Society

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