Date of Original Version

5-23-2001

Type

Article

Published In

Journal of Mathematical Logic 2 (1): 91-112, 2002.

Rights Management

All Rights Reserved

Abstract or Description

The notion of a function from ℕ to ℕ defined by recursion on ordinal notations is fundamental in proof theory. Here this notion is generalized to functions on the universe of sets, using notations for well orderings longer than the class of ordinals. The generalization is used to bound the rate of growth of any function on the universe of sets that is Σ1-definable in Kripke–Platek admissible set theory with an axiom of infinity. Formalizing the argument provides an ordinal analysis.

DOI

10.1142/S0219061302000126

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Philosophy Commons

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