On a Question of Jaegers

Vassilios Gregoriades

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arXiv · 1905.09609

On a Question of Jaegers

Vassilios Gregoriades

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Abstract

We show that there exists a positive arithmetical formula $\psi(x,R)$, where $x \in \omega$, $R \subseteq \omega$, with no hyperarithmetical fixed point. This answers a question of Gerhard J\"{a}ger. As corollaries we obtain results on the proof-theoretic strength of the Kripke-Platek set theory; the fixed points of monotone functions in chain-complete partial orders; the non-Borel uniformization of Borel sets; and the hyperdegrees of fixed points of positive formulae. Further we prove a Suslin-Kleene type result for the specific encoding of the hyperarithmetical sets that we are using.

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Vassilios Gregoriades. 2019-05-23. On a Question of Jaegers. https://arxiv.org/abs/1905.09609

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