Author:
Freund Anton,Rathjen Michael
Abstract
AbstractWe 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 $$\Pi ^1_1$$
Π
1
1
-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):431–454, 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.
Funder
Julius-Maximilians-Universität Würzburg
Publisher
Springer Science and Business Media LLC
Subject
General Physics and Astronomy,General Mathematics
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