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Pseudo-complements and ordinal logics based on consistency statements

Published online by Cambridge University Press:  12 March 2014

Robert A. Di Paola
Robert A. Di Paola*
Affiliation:
University of California, Los Angeles
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Extract

Following [1] we write {n} for the nth recursively enumerable (re) set; that is, {n} = {x|VyT(n, x, y)}. By a “pair (T, α)” we mean a consistent re extension T of Peano arithmetic P and an RE-formula α which numerates the non-logical axioms of T in P [4]. Given a pair (T, α) and a particular formula which binumerates the Kleene T predicate in P, there can be defined a primitive recursive function Nα such that and which has the additional property that {Nα(Nα(n))} = ø for all n.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 31 , Issue 3 , 02 September 1966 , pp. 359 - 364
Copyright
Copyright © Association for Symbolic Logic 1996

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References

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