Boundedness theorems for flowers and sharps-Reference-Cited by-同舟云学术

Boundedness theorems for flowers and sharps

Published:2022-06-10 Issue:9 Volume:150 Page:3973-3988
ISSN:0002-9939
Container-title:Proceedings of the American Mathematical Society
language:en
Short-container-title:Proc. Amer. Math. Soc.

Author:

Aguilera J.,Freund A.,Rathjen M.,Weiermann A.

Abstract

We show that the Σ 1 1 \Sigma ^1_1 - and Σ 2 1 \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].

Funder

Austrian Science Fund

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Link

https://www.ams.org/proc/2022-150-09/S0002-9939-2022-15859-6/proc15859_AM.pdf

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