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Interpreting true arithmetic in the local structure of the enumeration degrees

Published online by Cambridge University Press:  12 March 2014

Hristo Ganchev  and
Mariya Soskova
Hristo Ganchev
Affiliation:
Sofia University, Faculty of Mathematics and Informatics, 5 James Bourchier Boulevard, 1164 Sofia, Bulgaria, E-mail: [email protected]
Mariya Soskova
Affiliation:
Sofia University, Faculty of Mathematics and Informatics, 5 James Bourchier Boulevard, 1164 Sofia, Bulgaria, E-mail: [email protected]
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Abstract

We show that the theory of the local structure of the enumeration degrees is computably isomorphic to the theory of first order arithmetic. We introduce a novel coding method, using the notion of a -pair, to code a large class of countable relations.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 77 , Issue 4 , December 2012 , pp. 1184 - 1194
Copyright
Copyright © Association for Symbolic Logic 2012

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References

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