Well ordering principles for iterated $$\Pi ^1_1$$-comprehension
Well ordering principles for iterated $$\Pi ^1_1$$-comprehension
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 $$\Pi ^1_1$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msubsup> <mml:mi>Π</mml:mi> <mml:mn>1</mml:mn> <mml:mn>1</mml:mn> </mml:msubsup> </mml:math> -comprehension and the existence of admissible sets, over weak base theories. Our work …