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REDUCIBILITY IN SOME CATEGORIES OF PARTIAL RECURSIVE OPERATORS
Author(s) -
Bianchini Caterina,
Sorbi Andrea
Publication year - 1992
Publication title -
mathematical logic quarterly
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.473
H-Index - 28
eISSN - 1521-3870
pISSN - 0942-5616
DOI - 10.1002/malq.19920380133
Subject(s) - morphism , mathematics , partial function , recursion (computer science) , set (abstract data type) , variable (mathematics) , object (grammar) , algebra over a field , μ operator , partially ordered set , pure mathematics , discrete mathematics , recursive functions , algorithm , computer science , mathematical analysis , artificial intelligence , programming language
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.