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REDUCIBILITY IN SOME CATEGORIES OF PARTIAL RECURSIVE OPERATORS

✍ Scribed by Caterina Bianchini; Andrea Sorbi

Publisher
John Wiley and Sons
Year
1992
Tongue
English
Weight
609 KB
Volume
38
Category
Article
ISSN
0044-3050

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✦ Synopsis

Abstract

We 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.

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