Well ordering principles for iterated Π¹₁-comprehension

2021/12/15 by Freund, Anton, Rathjen, Michael · 1 citation
#03B30 #03D60 #03E10 #03F15 #03F35 #FOS: Mathematics #Logic (math.LO)

paper · doi:10.48550/arxiv.2112.08005

Abstract

We introduce ordinal collapsing principles that are inspired by proof theory but have a set theoretic flavor. These principles are shown to be equivalent to iterated Π¹₁-comprehension and the existence of admissible sets, over weak base theories. Our work extends a previous result on the non-iterated case, which had been conjectured in Montalbán's "Open questions in reverse mathematics" (Bull. Symb. Log. 17(3)2011). This previous result has already been applied to the reverse mathematics of combinatorial and set theoretic principles. The present paper is a significant contribution to a general approach that connects these fields.

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• Ordinal Analysis of Well-Ordering Principles, Well Quasi-Orders Closure Properties, and Σ_n-Collection Schema

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