The main result of this paper is the equivalence of several definition schemas of bar recursion occurring in the literature on functionals of finite type. We present the theory of functionals of finite type, in [T] denoted by q f W E H A '~ which is necessary for giving the equivalence proofs. Moreover we prove two results on this theory that cannot be… (More)

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Provably recursive functionals of analysis: a consistency proof of analysis by an extension of principles formulated in current intuitionistic mathematics