Σ1-Collection and the finite injury priority method

  • Theodore A. Slaman
  • W. Hugh Woodin
Conference paper
Part of the Lecture Notes in Mathematics book series (LNM, volume 1388)

Abstract

We show that there is an intermediate recursively enumerable Turing degree in every model of P+BΣ1. The proof is not uniform, depending on whether IΣ1 holds. There is a model of P+BΣ1 in which there is a least recursively enumerable degree strictly above the recursive degree. Thus, the Sacks Splitting Theorem cannot be proven in P+BΣ1.

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Copyright information

© Springer-Verlag 1989

Authors and Affiliations

  • Theodore A. Slaman
    • 1
    • 2
  • W. Hugh Woodin
    • 1
    • 2
  1. 1.Department of MathematicsThe University of ChicagoChicagoUSA
  2. 2.Department of MathematicsThe California Institute of TechnologyPasadenaUSA

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