Recursiveness

A-enumerable admissible subcategory assume axioms bijection called characteristic function class of sets cofinal conjugation consider Corollary 1.2 countable cylindrification denote disjoint domains distinguished subcategory enumerable sets establishes a bijection EXERCISE 2.1 exponential of k₁ finite follows from Proposition formulas free monoid full subcategory function f Further g and h g-¹h graph h(dx h₁ identity implies inclusion integer isomorphism of categories left exponential left successor logical functions monoid morphism N¹+r notation Nr+1 Nr+2 partial function primitive recursive functions primitive recursive isomorphism Proposition 2.2 recursively enumerable relation f right exponential Right successors satisfies condition selector smallest element subcategories of R(W successor function suffices to show surjection T-primitive T-recursive Theorem 1.2 uf)x unique function verify W⁰ Wr+1 Wr+s