Realizability with a Local Operator of A.M. Pitts

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Abstract

We study a notion of realizability with a local operator JJ which was first considered by A.M. Pitts in his thesis [7]. Using the Suslin–Kleene theorem, we show that the representable functions for this realizability are exactly the hyperarithmetical (Δ11) functions.

We show that there is a realizability interpretation of nonstandard arithmetic, which, despite its classical character, lives in a very non-classical universe, where the Uniformity Principle holds and König's Lemma fails. We conjecture that the local operator gives a useful indexing of the hyperarithmetical functions.
Original languageEnglish
Pages (from-to)237-243
Number of pages7
JournalTheoretical Computer Science
Volume546
Issue number27
DOIs
Publication statusPublished - 2014

Keywords

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