Provable Fixed Points
Copyright policy )Provable Fixed Points
The paper establishes some general conditions under wich a formula A(p) has only provable fixed points in Guaspari-Solovay modal logic of provability R. This result is used to give another proof of Parikh's theorem: For each natural number \(k\geq 1\) there is an arithmetical sentence A, provable in PA, such that \(\square^ kA\) has a much shorter proof than \(\square^ mA\) for any \(m
- University of Amsterdam Netherlands
- University of Siena Italy
- University of Siena Italy
First-order arithmetic and fragments, provable fixed points, Guaspari-Solovay modal logic of provability, proof, Gödel numberings and issues of incompleteness, Parikh's theorem, Modal logic (including the logic of norms)
First-order arithmetic and fragments, provable fixed points, Guaspari-Solovay modal logic of provability, proof, Gödel numberings and issues of incompleteness, Parikh's theorem, Modal logic (including the logic of norms)
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