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Some theorems on extensions of arithmetic1

Published online by Cambridge University Press:  12 March 2014

Robert A. Di Paola
Robert A. Di Paola*
Affiliation:
University of California, Los Angeles
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Extract

In this paper we study some of the consequences of adding as new axioms to consistent re (recursively enumerable) extensions T of Peano arithmetic P sentences undecidable in T of the Π10 variety, as are those one naturally comes upon. The question arises: how much can two extensions “differ” when each is obtained by adding just once distinct Π10 sentences undecidable in T? We shall show that if T is as stated above, we can find extensions T1 and T2, constructed very simply from T, having the property that if (A, B) is any pair of re sets with recursive intersection, there can be found a Π10 formula of P which represents A in T1 and B in T2.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 32 , Issue 2 , August 1967 , pp. 180 - 189
Copyright
Copyright © Association for Symbolic Logic 1967

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References

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