Bar recursion in classical realisability: dependent choice and continuum hypothesis
JL Krivine - arXiv preprint arXiv:1502.00112, 2015 - arxiv.org
arXiv preprint arXiv:1502.00112, 2015•arxiv.org
This paper is about the bar recursion operator in the context of classical realizability. After
the pioneering work of Berardi, Bezem & Coquand [1], T. Streicher has shown [10], by
means of their bar recursion operator, that the realizability models of ZF, obtained from usual
models of $\lambda $-calculus (Scott domains, coherent spaces,...), satisfy the axiom of
dependent choice. We give a proof of this result, using the tools of classical realizability.
Moreover, we show that these realizability models satisfy the well ordering of $\mathbb {R} …
the pioneering work of Berardi, Bezem & Coquand [1], T. Streicher has shown [10], by
means of their bar recursion operator, that the realizability models of ZF, obtained from usual
models of $\lambda $-calculus (Scott domains, coherent spaces,...), satisfy the axiom of
dependent choice. We give a proof of this result, using the tools of classical realizability.
Moreover, we show that these realizability models satisfy the well ordering of $\mathbb {R} …
This paper is about the bar recursion operator in the context of classical realizability. After the pioneering work of Berardi, Bezem & Coquand [1], T. Streicher has shown [10], by means of their bar recursion operator, that the realizability models of ZF, obtained from usual models of -calculus (Scott domains, coherent spaces, . . .), satisfy the axiom of dependent choice. We give a proof of this result, using the tools of classical realizability. Moreover, we show that these realizability models satisfy the well ordering of and the continuum hypothesis These formulas are therefore realized by closed -terms. This allows to obtain programs from proofs of arithmetical formulas using all these axioms.
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