All realizability is relative

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چکیده

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All realizability is relative

We introduce a category of basic combinatorial objects, encompassing PCAs and locales. Such a basic combinatorial object is to be thought of as a pre-realizability notion. To each such object we can associate an indexed preorder, generalizing the construction of triposes for various notions of realizability. There are two main results: first, the characterization of triposes which arise in this...

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ژورنال

عنوان ژورنال: Mathematical Proceedings of the Cambridge Philosophical Society

سال: 2006

ISSN: 0305-0041,1469-8064

DOI: 10.1017/s0305004106009352