Ordinal analysis by transformations

Henry Towsner
2009 Annals of Pure and Applied Logic  
The technique of using infinitary rules in an ordinal analysis has been one of the most productive developments in ordinal analysis. Unfortunately, one of the most advanced variants, the Buchholz Ω µ rule, does not apply to systems much stronger than Π 1 1comprehension. In this paper, we propose a new extension of the Ω rule using gametheoretic quantifiers. We apply this to a system of inductive definitions with at least the strength of a recursively inaccessible ordinal.
doi:10.1016/j.apal.2008.09.011 fatcat:4psauotquvag5ofq74jpazfcwe