Minimal Pair Constructions and Iterated Trees of Strategies

  • S. Lempp
  • M. Lerman
  • F. Weber
Part of the Progress in Computer Science and Applied Logic book series (PCS, volume 12)


We use the iterated trees of strategies approach developed in [LL1], [LL2] to prove some theorems about minimal pairs. In Section 1-3, we show how to use these methods to prove the Minimal Pair Theorem of Lachlan [L] and Yates [Y]:

Theorem 3.4 (Minimal Pair). There exist nonrecursive r.e. degreesaandbsuch thata λ b = 0.


Basic Module Minimal Pair True Path Finite Tree Finite Outcome 
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Copyright information

© Springer Science+Business Media New York 1993

Authors and Affiliations

  • S. Lempp
    • 1
  • M. Lerman
    • 2
  • F. Weber
    • 3
  1. 1.Department of MathematicsUniversity of WisconsinMadisonUSA
  2. 2.Department of MathematicsUniversity of ConnecticutStorrsUSA
  3. 3.Department of MathematicsConcordia University, WisconsinMequonUSA

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