The disjunction property implies the numerical existence property.
نویسنده
چکیده
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.
منابع مشابه
CZF has the Disjunction and Numerical Existence Property
This paper proves that the disjunction property, the numerical existence property and Church’s rule hold true for Constructive Zermelo-Fraenkel Set Theory, CZF, and also for the theory CZF augmented by the Regular Extension Axiom. As to the proof technique, it features a self-validating semantics for CZF that combines extensional Kleene realizability and truth. MSC:03F50, 03F35
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ورودعنوان ژورنال:
- Proceedings of the National Academy of Sciences of the United States of America
دوره 72 8 شماره
صفحات -
تاریخ انتشار 1975