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- W1469365530 abstract "This chapter describes the Friedman slash and Freyd covers and provides a proof that F* can be described in purely categorical terms from the Freyd cover from which Friedman's method can be reconstructed. Kleene's method [K] for proving the disjunction and existence properties (DP, EP) for HA was further developed and extended to intuitionistic type theory. Freyd independently gave an elegant proof of DP and EP for higher-order intuitionistic arithmetic (HAH), avoiding explicit syntactic constructions of but relying instead on general topos-theoretic facts on glueing of toposes. Both methods are essentially the same, by defining an elementary topos that embodies Friedman's notion of realizability and then showing that this topos is a subtopos of the topos (SetsCr) obtained by glueing the free topos and the topos of Sets along the global section functor F→Sets. Thus, Freyd's use of retracts and Friedman's impredicative assignment of indices turn out to be one and the same process, a fact that was called “a remarkable resemblance.”" @default.
- W1469365530 created "2016-06-24" @default.
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- W1469365530 date "1982-01-01" @default.
- W1469365530 modified "2023-09-27" @default.
- W1469365530 title "A Note on the Friedman Slash and Freyd Covers" @default.
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- W1469365530 doi "https://doi.org/10.1016/s0049-237x(09)70142-9" @default.
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