General Recursion Theory: An Axiomatic Approach |
Contents
On the Choice of Correct Notions for the General Theory | 3 |
0 | 11 |
Combinatorial Part | 19 |
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1-section a₁ admissible ordinals admissible sets argument assume assumption B-recursive b₁ basic Chapter characteristic function clauses computable function computation domain computation theory construction countable defined e₁ enumeration exists function f hence higher types hyperarithmetic hyperarithmetic theory immediate subcomputations inductive definition inductive operator infinite theory introduced K₂ Kechris Kleene Kleene-recursion L-subconstructive least fixed-point Lemma Let f limit ordinal Mahlo Moldestad monotone Moschovakis normal type-2 notion O-computable O-finite set ordinal p-normal partial functions PR(L PR[f PR[g precomputation theory prewellordering prewellordering property primitive recursive primitive recursive function proof Proposition prove quantifiers R-admissible reader recursion in higher recursion theory recursive function relation Remark result Section selection operator semicomputable set set theory set-recursive Spector class Spector theory stage strongly finite structure subset Theorem Tp(S tuples v₁ weakly well-foundedness x₁ y₁ Σ₁