REDUCIBILITY IN SOME CATEGORIES OF PARTIAL RECURSIVE OPERATORS
Copyright policy )REDUCIBILITY IN SOME CATEGORIES OF PARTIAL RECURSIVE OPERATORS
AbstractWe consider two categories with one object, namely the set of all partial functions of one variable from the set of natural numbers into itself; the morphisms are the partial recursive operators in one case, and certain continuous partial mappings in the other case. We show that these categories are recursion categories and we characterize the domains and the complete domains. Some observations are made on a notion of reducibility obtained by using the total morphisms of these categories, and, subsequently, the general recursive operators.
- University of Siena Italy
Categories of machines, automata, partial recursive operators, reducibility, partial recursive operator, 004, 510, dominical categories; partial recursive operators; Recursion categories, recursion categories, Recursion categories, completeness, dominical categorie, creativeness, dominical categories, Abstract and axiomatic computability and recursion theory, Theory of numerations, effectively presented structures, domains
Categories of machines, automata, partial recursive operators, reducibility, partial recursive operator, 004, 510, dominical categories; partial recursive operators; Recursion categories, recursion categories, Recursion categories, completeness, dominical categorie, creativeness, dominical categories, Abstract and axiomatic computability and recursion theory, Theory of numerations, effectively presented structures, domains
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