On a Subrecursive Hierarchy and Primitive Recursive Degrees |
Common terms and phrases
Anba h b,a arbitrary one-place function assumed functions ba b,a based on index C₁ c₂ complete sequence completes the proof computation based constant function course-of-values induction course-of-values recursion Define the function DOCTOR OF PHILOSOPHY exp tr² exponent fin(y follows by induction function b,c function defined function primitive recursive function value Furthermore given general recursive h-types h₂ HIERARCHY AND PRIMITIVE hypothesis of induction k-recursive Lemma limit notation m²,n majorizes the one-place monotone increasing monotone non-decreasing one-place primitive recursive ordinal notations ordinals less P₁ PAUL AXT pr b,a predicate or set primitive recursive degree primitive recursive function recursive in Anba recursive in h recursive in pr(b,a recursively as follows representing function schemata semi-lattice sequences of notations SUBRECURSIVE HIERARCHY suffices to take thesis uniqueness property holds University of Wisconsin