Classical and Intuitionistic Arithmetic with Higher Order Comprehension Coincide on Inductive Well-Foundedness
نویسنده
چکیده
Assume that we may prove in Arithmetic with Comprehension axiom that a primitive recursive binary relation R is well-founded, using the inductive definition of well-founded. In this paper we prove that the proof that R is well-founded may be made intuitionistic. Our result generalizes to any implication between such formulas. We conclude that if we are able to formulate any mathematical problem as the fact that some primitive recursive relation is well-founded, then intuitionistic and classical provability coincide, and for such a statement we may always find an intuitionistic proof, if we may find a proof at all. 1998 ACM Subject Classification F.4.1 Mathematical Logic
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تاریخ انتشار 2015