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Ordinal diagrams for Π3-reflection
Published online by Cambridge University Press: 12 March 2014
Abstract
In this paper we introduce a recursive notation system O(Π3) of ordinals. An element of the notation system is called an ordinal diagram. The system is designed for proof theoretic study of theories of Π3-reflection. We show that for each α < Ω in O(Π3) a set theory KP Π3 for Π3-reflection proves that the initial segment of O(Π3) determined by α is a well ordering. Proof theoretic study for such theories will be reported in [ 4].
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- Copyright © Association for Symbolic Logic 2000
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