Abstract:Let's fix a reasonable subsystem T of arithmetic; why are natural extensions of T pre-well-ordered by consistency strength? In previous work, an approach to this question was proposed. The goal of this work was to classify the recursive functions that are monotone with respect to the Lindenabum algebra of T . According to an optimistic conjecture, roughly, every such function must be equivalent to an iterate Con α T of the consistency operator in the limit.In previous work the author established the first case… Show more
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