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Published 1988 | metadata_only
Book Section - Chapter

Subsets of ℵ_1 constructible from a real


The purpose of this paper is to give a necessary and sufficient condition for a subset of ℵ_1 to be constructible from a real in terms of structural properties of the code set of A, valid under the condition that an appropriate measurable cardinal exists. This can be combined with recent results of Woodin to provide upper bounds for the consistency strength, of theories of the form ZFC + ∀x Є ω^ω(x^# exists)+ "every subset of ℵ_1 with code set in Г is constructible from a real," for various pointclasses Г.

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© 1988 Springer. Research partially supported by NSF Grants MCS-8117804 and DMS-8416349.

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August 19, 2023
August 19, 2023