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A souslin operation for Π 12

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Abstract

Throughout this paper we assume the existence of a measureable cardinal. Membership in a Π 12 set of reals is shown to be equivalent to the existence of an infinite path in a tree ℐ* of pairs of finite sequences of natural numbers and ordinals. This is used to prove that every Π 12 relation can be uniformized by a Π 12 function. One gets that under certain assumptions the Shoenfield Absoluteness Theorem holds for Σ 13 statements, that Π 13 sets include perfect subsets and that Σ 13 sets are Lebesgue measureable and have the Baire Property.

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Authors and Affiliations

  1. University of California, Los-Angeles

    Richard Mansfield

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  1. Richard Mansfield
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Mansfield, R. A souslin operation for Π 12 . Israel J. Math. 9, 367–379 (1971). https://doi.org/10.1007/BF02771687

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  • DOI: https://doi.org/10.1007/BF02771687

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