An ordinal analysis of admissible set theory using recursion on ordinal notations

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



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Jeremy Avigad
Carnegie Mellon University

References found in this work

Saturated models of universal theories.Jeremy Avigad - 2002 - Annals of Pure and Applied Logic 118 (3):219-234.
Update Procedures and the 1-Consistency of Arithmetic.Jeremy Avigad - 2002 - Mathematical Logic Quarterly 48 (1):3-13.

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