Boundedness theorems for flowers and sharps
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- by J. P. Aguilera, A. Freund, M. Rathjen and A. Weiermann
- Proc. Amer. Math. Soc. 150 (2022), 3973-3988
- DOI: https://doi.org/10.1090/proc/15859
- Published electronically: June 10, 2022
Abstract:
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].References
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Bibliographic Information
- J. P. Aguilera
- Affiliation: Institute of discrete Mathematics and Geometry, Technical University of Vienna, Wiedner Hauptstrasse 8-10, 1040 Vienna, Austria; and Department of Mathematics, Ghent University, Krijgslaan 281, 9000 Ghent, Belgium
- MR Author ID: 1199300
- Email: aguilera@logic.at
- A. Freund
- Affiliation: Department of Mathematics, Technical University of Darmstadt, Schlossgartenstrasse 7, 64289 Darmstadt, Germany
- MR Author ID: 1106402
- ORCID: 0000-0002-5456-5790
- Email: freund@mathematik.tu-darmstadt.de
- M. Rathjen
- Affiliation: School of Mathematics, University of Leeds, Leeds LS2 9JT, United Kingdom
- MR Author ID: 290825
- Email: rathjen@maths.leeds.ac.uk
- A. Weiermann
- Affiliation: Department of Mathematics, Ghent University, Krijgslaan 281, 9000 Ghent, Belgium
- MR Author ID: 317296
- ORCID: 0000-0002-5561-5323
- Email: andreas.weiermann@ugent.be
- Received by editor(s): May 19, 2021
- Received by editor(s) in revised form: September 6, 2021
- Published electronically: June 10, 2022
- Additional Notes: The first author was partially supported by FWF grant I4513N and FWO grant 3E017319. The second author was funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation), Project number 460597863. The third author was partially supported by JTF grant 60842. The fourth author was partially supported by FWO grants G0E2121N and G030620N
- Communicated by: Vera Fischer
- © Copyright 2022 J. P. Aguilera; A. Freund; M. Rathjen; A. Weiermann
- Journal: Proc. Amer. Math. Soc. 150 (2022), 3973-3988
- MSC (2020): Primary 03F15; Secondary 03E15, 03E45, 18A35, 18B35
- DOI: https://doi.org/10.1090/proc/15859
- MathSciNet review: 4446245