A note on indicator-functions
Author: J. Myhill
Journal: Proc. Amer. Math. Soc. 39 (1973), 181-183
MSC: Primary 02C15; Secondary 02K05
MathSciNet review: 0432406
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Abstract: A system has the existence-property for abstracts (existence property for numbers, disjunction-property) if whenever for some abstract for some numeral ; if whenever or are closed). We show that the existence-property for numbers and the disjunction property are never provable in the system itself; more strongly, the (classically) recursive functions that encode these properties are not provably recursive functions of the system. It is however possible for a system (e.g., ) to prove the existence-property for abstracts for itself.
-  J. Myhill, Some properties of intuitionistic Zermelo-Frankel set-theory, Proceedings of the Logic Conference at Cambridge, August 1971.
- J. Myhill, Some properties of intuitionistic Zermelo-Frankel set-theory, Proceedings of the Logic Conference at Cambridge, August 1971.
Keywords: Existence and disjunction-properties, realizability
Article copyright: © Copyright 1973 American Mathematical Society