Israel Journal of Mathematics

, Volume 121, Issue 1, pp 1–28 | Cite as

2 Induction and infinite injury priority arguments, part III: Prompt sets, minimal pairs and Shoenfield’s Conjecture

  • C. T. Chong
  • Lei Qian
  • Theodore A. Slaman
  • Yue Yang
Article

Abstract

We prove that in everyB∑ 2 model (one satisfies ∑2 collection axioms but not ∑2 induction), every recursively enumerable (r.e.) set is either prompt or recursive. Consequently, over the base theory ∑2 collection, the existence of r.e. minimal pairs is equivalent to ∑2 induction. We also refute Shoenfield’s Conjecture inB∑ 2 models.

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Copyright information

© Hebrew University 2001

Authors and Affiliations

  • C. T. Chong
    • 1
  • Lei Qian
    • 2
  • Theodore A. Slaman
    • 3
  • Yue Yang
    • 4
  1. 1.Department of Mathematics, Faculty of ScienceNational University of SingaporeSingapore
  2. 2.Department of Mathematics, Faculty of ScienceNational University of SingaporeSingapore
  3. 3.Department of MathematicsUniversity of California BerkeleyBerkeleyUSA
  4. 4.Department of Mathematics, Faculty of ScienceNational University of SingaporeSingapore

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