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On the derivability of instantiation properties

Published online by Cambridge University Press:  12 March 2014

Harvey Friedman
Harvey Friedman*
Affiliation:
State University of New York at BuffaloAmherst, New York 14226
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Abstract

Every recursively enumerable extension of arithmetic which obeys the disjunction property obeys the numerical existence property [Fr, 1]. The requirement of recursive enumerability is essential. For extensions of intuitionistic second order arithmetic by means of sentences (in its language) with no existential set quantifiers, the numerical existence property implies the set existence property. The restriction on existential set quantifiers is essential. The numerical existence property cannot be eliminated, but in the case of finite extensions of HAS, can be replaced by a weaker form of it. As a consequence, the set existence property for intuitionistic second order arithmetic can be proved within itself.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 42 , Issue 4 , December 1977 , pp. 506 - 514
Copyright
Copyright © Association for Symbolic Logic 1977

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References

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