Well ordering principles for iterated ∏ 1 1-comprehension

• Anton Freund ^[1] ; Michael Rathjen ^[2]
  1. [1] University of Würzburg

     University of Würzburg

     Kreisfreie Stadt Würzburg, Alemania

     
  2. [2] University of Leeds

     University of Leeds

     Reino Unido

     
• Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 29, Nº. 5, 2023
• Idioma: inglés
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• Resumen

  • 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 ∏ 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.