On the consistency strength of $\mathsf {MM}(\omega _1)$
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- by Natasha Dobrinen, John Krueger, Pedro Marun, Miguel Angel Mota and Jindrich Zapletal;
- Proc. Amer. Math. Soc. 152 (2024), 2229-2237
- DOI: https://doi.org/10.1090/proc/16718
- Published electronically: March 7, 2024
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Abstract:
We prove that the consistency of Martin’s Maximum restricted to partial orders of cardinality $\omega _1$ follows from the consistency of $\mathsf {ZFC}$.References
- D. Asperó and M. Golshani, The proper forcing axiom for $\aleph _1$-sized posets, Prikry-type proper forcing, and the size of the continuum, Preprint, arXiv:2209.01395, 2023.
- David Asperó and Miguel Angel Mota, Forcing consequences of PFA together with the continuum large, Trans. Amer. Math. Soc. 367 (2015), no. 9, 6103–6129. MR 3356931, DOI 10.1090/S0002-9947-2015-06205-9
- M. Foreman, M. Magidor, and S. Shelah, Martin’s maximum, saturated ideals, and nonregular ultrafilters. I, Ann. of Math. (2) 127 (1988), no. 1, 1–47. MR 924672, DOI 10.2307/1971415
- H. Sakai, $\omega _1$-stationary preserving poset of size $\omega _1$ which is not semi-proper, available at http://www2.kobe-u.ac.jp/~hsakai/, unpublished.
- Saharon Shelah, Proper and improper forcing, 2nd ed., Perspectives in Mathematical Logic, Springer-Verlag, Berlin, 1998. MR 1623206, DOI 10.1007/978-3-662-12831-2
- Saharon Shelah, Semiproper forcing axiom implies Martin maximum but not $\textrm {PFA}^+$, J. Symbolic Logic 52 (1987), no. 2, 360–367. MR 890443, DOI 10.2307/2274385
Bibliographic Information
- Natasha Dobrinen
- Affiliation: Department of Mathematics, University of Notre Dame, Notre Dame, Indiana 46556
- MR Author ID: 702137
- Email: ndobrine@nd.edu
- John Krueger
- Affiliation: Department of Mathematics, University of North Texas, Denton, Texas 76203
- MR Author ID: 720328
- Email: jkrueger@unt.edu
- Pedro Marun
- Affiliation: Department of Mathematical Sciences, Carnegie Mellon University, Pittsburgh, Pennsylvania 15213
- ORCID: 0009-0000-1924-1136
- Email: pmarun@andrew.cmu.edu
- Miguel Angel Mota
- Affiliation: Departamento de Matemáticas, ITAM, 01080, Mexico City, Mexico
- MR Author ID: 1031552
- Email: motagaytan@gmail.com
- Jindrich Zapletal
- Affiliation: Department of Mathematics, University of Florida, Gainesville, Florida 32611
- MR Author ID: 359571
- ORCID: 0000-0003-3437-5073
- Email: zapletal@ufl.edu
- Received by editor(s): July 12, 2023
- Received by editor(s) in revised form: October 25, 2023
- Published electronically: March 7, 2024
- Additional Notes: This paper was originally conceived during the workshop From $\aleph _2$ to Infinity sponsored by the American Institute of Mathematics and the National Science Foundation.
The first author was supported by the National Science Foundation under grant NSF DMS-1901753. The second author was supported by the Simons Foundation under Grant 631279. - Communicated by: Vera Fischer
- © Copyright 2024 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 152 (2024), 2229-2237
- MSC (2020): Primary 03E35, 03E50
- DOI: https://doi.org/10.1090/proc/16718
- MathSciNet review: 4728486