'Flexible' Predicates of Formal Number Theory |
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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__

- 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.
- 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.
- 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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