Embeddings in the strong reducibilities between 1 and npm

Watson, Phil (1997) Embeddings in the strong reducibilities between 1 and npm. Mathematical Logic Quarterly, 43 (4). pp. 559-568. ISSN 0942-5616 . (The full text of this publication is not currently available from this repository. You may be able to access a copy if URLs are provided)

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We consider the strongest (most restricted) forms of enumeration reducibility, those that occur between 1- and npm-reducibility inclusive. By defining two new reducibilities (which we call n1- and ni-reducibility) which are counterparts to 1- and i-reducibility (respectively) in the same way that nm- and npm- reducibility are counterparts to m- and pm-reducibility respectively, we bring out the structure (under the natural relation on reducibilities `strong with respect to') of the strong reducibilities. By further restricting n1- and nm-reducibility we are able to define infinite families of reducibilities which isomorphically embed the r.e. Turing degrees. Thus the many well-known results in the theory of the r.e. Turing degrees have counterparts in the theory of strong reducibilities. We are also able to positively answer the question of whether there exist distinct reducibilities y and z between e and m such that there exists a non-trivial y-contiguous z degree.

Item Type: Article
Uncontrolled keywords: recursive function theory, enumeration degrees
Subjects: Q Science > QA Mathematics (inc Computing science) > QA 76 Software, computer programming,
Divisions: Faculties > Science Technology and Medical Studies > School of Computing > Theoretical Computing Group
Depositing User: Mark Wheadon
Date Deposited: 02 Aug 2009 23:25
Last Modified: 25 Jun 2014 11:07
Resource URI: https://kar.kent.ac.uk/id/eprint/21428 (The current URI for this page, for reference purposes)
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