Diagonalization in double frames

Logica Universalis 4 (1):31-39 (2010)
Abstract
We consider structures of the form, where Φ and Ψ are non-empty sets and is a relation whose domain is Ψ. In particular, by using a special kind of a diagonal argument, we prove that if Φ is a denumerable recursive set, Ψ is a denumerable r.e. set, and R is an r.e. relation, then there exists an infinite family of infinite recursive subsets of Φ which are not R -images of elements of Ψ. The proof is a very elementary one, without any reference even to e.g. the -theorem. Some consequences of the main result are also discussed
Keywords Diagonalization  double frames  incompleteness
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DOI 10.1007/s11787-010-0012-3
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References found in this work BETA
Classical Recursion Theory: The Theory of Functions and Sets of Natural Numbers.Piergiorgio Odifreddi - 1989 - Sole Distributors for the Usa and Canada, Elsevier Science Pub. Co..
Fundamentals of Mathematical Logic.Peter G. Hinman - 2007 - Bulletin of Symbolic Logic 13 (3):363-365.

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