Boundedness theorems for flowers and sharps

Boundedness theorems for flowers and sharps

We show that the \Sigma ^1_1- and \Sigma ^1_2-boundedness theorems extend to the category of continuous dilators. We then apply these results to conclude the corresponding theorems for the category of sharps of real numbers, thus establishing another connection between Proof Theory and Set Theory, a...

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Veröffentlicht in:Proceedings of the American Mathematical Society 2022-09, Vol.150 (9), p.3973-3988
Hauptverfasser: Aguilera, J., Freund, A., Rathjen, M., Weiermann, A.
Format: Artikel
Sprache:eng
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Zusammenfassung:We show that the \Sigma ^1_1- and \Sigma ^1_2-boundedness theorems extend to the category of continuous dilators. We then apply these results to conclude the corresponding theorems for the category of sharps of real numbers, thus establishing another connection between Proof Theory and Set Theory, and extending work of Girard-Normann [J. Symbolic Logic 57 (1992), pp. 659–676] and Kechris-Woodin [Ann. Pure Appl. Logic 52 (1991), pp. 93–97].
ISSN:0002-9939
1088-6826
DOI:10.1090/proc/15859