Realizability with a Local Operator of A.M. Pitts

Jaap van Oosten

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arXiv · 1301.0735

Realizability with a Local Operator of A.M. Pitts

Jaap van Oosten

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Abstract

We study a notion of realizability with a local operator J which was first considered by A.M. Pitts in his thesis. Using the Suslin-Kleene theorem, we show that the representable functions for this realizability are exactly the hyperarithmetical functions. We show that there is a realizability interpretation of nonstandard arithmetic, which, despite its classical character, lives in a very nonclassical universe, where the Uniformity Principle holds and Konig's Lemma fails. We conjecture that the local operator gives a useful indexing of the hyperarithmetical functions.

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BibTeX RIS

Jaap van Oosten. 2013-01-04. Realizability with a Local Operator of A.M. Pitts. https://arxiv.org/abs/1301.0735

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