Applications of cut-free infinitary derivations to generalized recursion theory

doi:10.1016/S0168-0072(97)00063-8

Annals of Pure and Applied Logic

Volume 94, Issues 1–3, 5 October 1998, Pages 7-19

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Abstract

We prove that the boundedness theorem of generalized recursion theory can be derived from the ω-completeness theorem for number theory. This yields a proof of the boundedness theorem which does not refer to the analytical hierarchy theorem.

MSC

03D60

03D55

03F05

Keywords

Cut-free infinitary derivations

Boundedness principles

Boundedness theorems

Recursive ordinals

Definable well-orderings