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The computation domain
Recursion on O
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2nd order admissible a-constructive ordinals a-gap with length a-reflecting abstract Kleene theory admissible ordinal argument list cartesian product characteristic function clause computable function convergent computation Corollary countable cp(a cp(x denoted element equality relation explicit definition finite lists finite number func function f HC(a HC(t Hence hereditarily consistent objects immediate subcomputations induction hypothesis least fixed point lemma Let f limit ordinal list of objects Mahlo monotone functional Moschovakis natural numbers nonempty subset normal computation theory normal list normal object objects of type On(cp Ord(f order type partial function partial recursive function prewellorderings with domain primitive recursive function proof of theorem proposition quantifiers recursive in F recursively enumerable second recursion theorem semicomputable sense of Kleene strongly finite subconstructive ordinals substitution supremum tion total function total objects Tp(i Tp(n type structure type symbol type with level weakly computable weakly finite weakly recursive