Turing invariant sets and the perfect set property

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Mathematical Logic Quarterly 66 (2):247-250 (2020)
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Abstract

We show that ZF + DC + “all Turing invariant sets of reals have the perfect set property” implies that all sets of reals have the perfect set property. We also show that this result generalizes to all countable analytic equivalence relations.

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10.1002/malq.202000005

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Citations of this work

Some Consequences of And.Yinhe Peng, W. U. Liuzhen & Y. U. Liang - 2023 - Journal of Symbolic Logic 88 (4):1573-1589.

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References found in this work

Turing determinacy and the continuum hypothesis.Ramez L. Sami - 1989 - Archive for Mathematical Logic 28 (3):149-154.
Turing cones and set theory of the reals.Benedikt Löwe - 2001 - Archive for Mathematical Logic 40 (8):651-664.

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