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Proceedings of the National Academy of Sciences of the United States of America logoLink to Proceedings of the National Academy of Sciences of the United States of America
. 1975 Aug;72(8):2877–2878. doi: 10.1073/pnas.72.8.2877

The disjunction property implies the numerical existence property

Harvey Friedman 1
PMCID: PMC432880  PMID: 16592266

Abstract

Any recursively enumerable extension of intuitionistic arithmetic which obeys the disjunction property obeys the numerical existence property. Any recursively enumerable extension of intuitionistic arithmetic proves its own disjunction property if and only if it proves its own inconsistency.

Keywords: intuitionism, arithmetic, formal systems, self reference

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