Computations in Higher Types |
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2nd order admissible a-constructive ordinals a-gap with length a-reflecting abstract Kleene theory admissible ordinal argument list characteristic function clause computation domain construction convergent computation Corollary countable denoted e}IV element equality relation explicit definition finite number fixed point func function defined function f HC(o Hence hereditarily consistent objects immediate subcomputations induction hypothesis Irlp L-computation lemma Let f limit ordinal list of objects Mahlo monotone functional Moschovakis natural numbers normal computation theory normal list objects of type Ord(f order type partial function prewellordering primitive recursive function proof of theorem proposition pwog(x quantifiers R₁(B recursive in F recursive in L recursively enumerable second recursion theorem semicomputable sense of Kleene strongly finite subindividuals substitution Suppose supremum tion total objects Tp(i Tp(n type structure type symbol weakly computable weakly finite weakly recursive ху