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Effectively extensible theories1

Published online by Cambridge University Press:  12 March 2014

Marian Boykan Pour-El
Marian Boykan Pour-El*
Affiliation:
University of Minnesota
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Extract

It is well known that Gödel's famous undecidability result may be viewed in the following strong form. Suppose we are given a specific presentation (i.e., a specific formulation in terms of axioms and rules of inference) of number theory. Then there exists an effective method which, when applied to a consistent axiomatizable extension of the theory yields an undecidable sentence of this extension. For distinct presentations the undecidable sentences obtained would be distinct. This is because the sentence constructed depends upon the notion of proof and hence ultimately upon the axioms and rules of inference—i.e., upon the specific presentation.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 33 , Issue 1 , 26 April 1968 , pp. 56 - 68
Copyright
Copyright © Association for Symbolic Logic 1968

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Footnotes

1

This paper was written while the author held grants awarded by the Institute for Advanced Study from funds the Institute derived from the National Science Foundation. The author wishes to express her sincere thanks to Professor Kurt Gödel for his continued interest over the years in the specific results of this paper.

References

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