An ordinal analysis of admissible set theory using recursion on ordinal notations
Journal of Mathematical Logic 2 (01):91-112 (2002)
| Abstract | 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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