General recursive function: Difference between revisions

Revision as of 18:09, 30 September 2005

Revision as of 20:38, 24 October 2005

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It is easy to see that this least search axiom (along with the simple primitive recursion axioms) implies the bounded search axiom of primitive recursion.

The set of ''partial recursive functions'' iskkis defined as the smallest set of partial functions of any [[arity]] from natural numbers to natural numbers which contains the zero, successor, and projection functions, and which is closed under composition, primitive recursion, and unbounded search.

The set of ''total recursive functions'' is the subset of partial recursive functions which are [[total function|total]].