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Some results on measure independent Gödel speed-ups1

Published online by Cambridge University Press:  12 March 2014

Martin K. Solomon
Martin K. Solomon*
Affiliation:
Graduate School of Business Administration, Rutgers UniversityNewark, New Jersey 07107
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Abstract

We study the measure independent character of Gödel speed-up theorems, in particular, we strengthen Arbib's necessary condition for the occurrence of a Gödel speed-up [2, p. 13] to an equivalence result and generalize Di Paola's speed-up theorem [4]. We also characterize undecidable theories as precisely those theories which possess consistent measure independent Gödel speed-ups and show that a theory τ2 is a measure independent Gödel speed-up of a theory τ1 if and only if the set of undecidable sentences of τ1 which are provable in τ2 is not recursively enumerable.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 43 , Issue 4 , December 1978 , pp. 667 - 672
Copyright
Copyright © Association for Symbolic Logic 1978

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Footnotes

1

Most of the results in this paper are taken from the author's Ph.D. Dissertation (Stevens Institute of Technology) which was written under the valuable supervision of Stephen L. Bloom.

The author is also grateful to Professor Bloom for his careful examination of this paper and to the referee for helpful suggestions.

References

REFERENCES

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