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On the T-degrees of partial functions

Published online by Cambridge University Press:  12 March 2014

Paolo Casalegno
Paolo Casalegno*
Affiliation:
Dipartimento di F1Losofia, Università di Pisa, 56100 Pisa, Italy
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Abstract

Let 〈, ≤ 〉 be the usual structure of the degrees of unsolvability and 〈, ≤ 〉 the structure of the T-degrees of partial functions defined in [7]. We prove that every countable distributive lattice with a least element can be isomorphically embedded as an initial segment of 〈, ≤ 〉: as a corollary, the first order theory of 〈, ≤ 〉 is recursively isomorphic to that of 〈, ≤ 〉. We also show that 〈, ≤ 〉 and 〈, ≤ 〉 are not elementarily equivalent.

Information

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 50 , Issue 3 , September 1985 , pp. 580 - 588
Copyright
Copyright © Association for Symbolic Logic 1985

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References

REFERENCES

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