Higher Recursion Theory |
Contents
Part A Hyperarithmetic Sets Chapter I Constructive Ordinals and II Sets 1 Analytical Predicates | 1 |
Notations for Ordinals 3 Effective Transfinite Recursion | 15 |
Recursive Ordinals 5 Ordinal Analysis of II Sets | 19 |
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a-cardinal a-finite admissible ordinal admissible set admits Moschovakis witnesses argument arithmetic Assume L(x B₁ bounded c₁ classical recursion theory cofinality construction converges Corollary countable definition denoted E-recursively enumerable effective transfinite recursion element encodes enumerable on L(x equivalent Exercise finite follows forcing formula Gandy selection gc(x Gödel number Hence hyperregular implies induction infinite initial segment injury Kleene Kleene's Lemma Let f metafinite natural enumeration negative requirements nonempty Normann one-one order definable ordertype ordinals less parameters partial E-recursive function Post's problem predicate prior to stage proof of Lemma proof of Theorem Proposition quantifiers recursion theory recursive function recursive ordinals recursively enumerable sets regular req 2ɛ satisfies Section sentence set of ordinals Show Slaman solution to Post's subset Suppose TC(x tp(a transfinite recursion Turing degrees Turing jump unbounded wellfounded wellordering Σ₁