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The equivalence of the disjunction and existence properties for modal arithmetic

Published online by Cambridge University Press:  12 March 2014

Harvey Friedman  and
Michael Sheard
Harvey Friedman
Affiliation:
Department of Mathematics, Ohio State University, Columbus, Ohio 43210
Michael Sheard
Affiliation:
Department of Mathematics, Saint Lawrence University, Canton, New York 13617
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Abstract

In a modal system of arithmetic, a theory S has the modal disjunction property if whenever S ⊢ □φ ∨ □ψ, either S ⊢ □φ or S ⊢ □ψ. S has the modal numerical existence property if whenever S ⊢ ∃x □φ(x), there is some natural number n such that S ⊢ □φ(n). Under certain broadly applicable assumptions, these two properties are equivalent.

Information

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 54 , Issue 4 , December 1989 , pp. 1456 - 1459
Copyright
Copyright © Association for Symbolic Logic 1989

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References

REFERENCES

[1] Friedman, H., The disjunction property implies the numerical existence property, Proceedings of the National Academy of Sciences of the United States of America, vol. 72 (1975), pp. 2877–2878.CrossRefGoogle ScholarPubMed
[2] Shapiro, S., Epistemic and intuitionistic arithmetic, Intensional mathematics (Shapiro, S., editor), North-Holland, Amsterdam, 1985, pp. 11–46.CrossRefGoogle Scholar