Abstract
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.
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Dietzfelbinger, M., Maass, W. (1985). Strong reducibilities in α- and β-recursion theory. In: Ebbinghaus, HD., Müller, G.H., Sacks, G.E. (eds) Recursion Theory Week. Lecture Notes in Mathematics, vol 1141. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0076216
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DOI: https://doi.org/10.1007/BFb0076216
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