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 admissible sets analysis argument assume assumption B-recursive basic Chapter characteristic function clauses computable function computation domain computation theory construction defined element enumeration exists finite function f hence higher types hyperarithmetic hyperarithmetic theory immediate subcomputations IND(C induction hypothesis inductive definition inductive operator infinite theory introduce K₂ Kechris Kleene recursion least fixed-point Lemma Let f limit ordinal Mahlo mapping monotone Moschovakis normal type-2 notation notion O-computable O-finite set O-semicomputable relations ordinal p-normal partial function PR(L PR[f PR[g precomputation theory prewellordering property primitive recursive primitive recursive function proof Proposition prove quantifiers R-admissible R₁ reader recursion in higher recursion theory recursive function Remark requirement result Section selection operator semicomputable set Spector class Spector theory stage Stoltenberg-Hansen strongly O-finite structure subset Theorem Tp(S tuples type-2 functional w₁ well-foundedness x₁ Y₁ Σ₁