'Flexible' Predicates of Formal Number Theory
Kripke (Saul)
Source: Proceedings of the American Mathematical Society, Vol. 13, No. 4 (Aug., 1962), pp. 647-650
Paper - Abstract

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Author’s Introduction

  1. The famous incompleteness theorem of Godel showed that a formal system containing the usual number theory must have an "undecidable" statement whose truth-value is not determined by the formal system.
  2. The present note gives an analogous theorem constructing predicates which are "flexible" in the sense that their extensions as sets are left undetermined by the formal system.
  3. We utilize the recursive-function-theoretic approach of Kleene; knowledge of his work is presupposed, and his notations and terminology will be used freely.

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