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Authors: Suzuki, Toshiyuki
鈴木, 利幸
Issue Date: 29-Jul-2010
Publisher: 高知工科大学
Journal Title: 高知工科大学紀要
Volume: 7
Issue: 1
Start Page: 109
End Page: 124
Abstract: The formal system in which the Peano’s axioms hold for numbers and there are quantifications over predicate variables is said to be classical analysis. In this system the real numbers are definable by predicators as certain sets of rational numbers and universal and existential statements about real numbers are formalizable. The formal system of elementary analysis is the subsystem of classical analysis which is restricted to the comprehension axioms for only elementary predicators in which no quantifiers over predicate variables are contained. And the ω-consistency of a formal system is a stronger property than the simple consistency of the system. We show that a normal form theorem for the formal system of elementary analysis which implies the ω-consistency of the system is proved by applying transfinite induction up to εε1.
Type: Departmental Bulletin Paper
URI: http://hdl.handle.net/10173/535
Appears in Collections:鈴木, 利幸 (SUZUKI, Toshiyuki)

Please use this identifier to cite or link to this item: http://hdl.handle.net/10173/535

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