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Provable fixed points. (English) Zbl 0661.03009
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 $$m<k$$.
Reviewer: S.Artemov

##### MSC:
 03B45 Modal logic (including the logic of norms) 03F40 Gödel numberings and issues of incompleteness 03F30 First-order arithmetic and fragments
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