Strong reducibilities in α- and β-recursion theory

  • Martin Dietzfelbinger
  • Wolfgang Maass
Conference paper
Part of the Lecture Notes in Mathematics book series (LNM, volume 1141)


We start an investigation of strong reducibilities in α- and β-recursion theory. In particular, we study Myhill's Theorem about recursive isomorphisms (A≤1 B & B≤1 A <=> A ≡ B), and show that it holds for a limit ordinal β if and only if σlcfβ=ω. (In particular, it fails for all admissible α>ω.) We point out a consequence for
-sets (n≥2) under V=L.


Strong Reducibility Partial Function Isomorphism Type Acceptable Numbering Recursion Theory 
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Copyright information

© Springer-Verlag 1985

Authors and Affiliations

  • Martin Dietzfelbinger
    • 1
  • Wolfgang Maass
    • 1
  1. 1.Department of Mathematics, Statistics and Computer ScienceUniversity of Illinois at ChicagoChicago

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