A note on the eightfold way
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- by Thomas Gilton and John Krueger
- Proc. Amer. Math. Soc. 148 (2020), 1283-1293
- DOI: https://doi.org/10.1090/proc/14771
- Published electronically: September 23, 2019
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Abstract:
Assuming the existence of a Mahlo cardinal, we construct a model in which there exists an $\omega _2$-Aronszajn tree, the $\omega _1$-approachability property fails, and every stationary subset of $\omega _2 \cap \text {cof}(\omega )$ reflects. This solves an open problem of Cummings et al. [J. Symb. Log. 83 (2018), no. 1, pp. 349–371]References
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Bibliographic Information
- Thomas Gilton
- Affiliation: Department of Mathematics, University of California, Los Angeles, Box 951555, Los Angeles, California 90095-1555
- MR Author ID: 1201642
- Email: tdgilton@math.ucla.edu
- John Krueger
- Affiliation: Department of Mathematics, University of North Texas, 1155 Union Circle #311430, Denton, Texas 76203
- MR Author ID: 720328
- Email: jkrueger@unt.edu
- Received by editor(s): January 9, 2019
- Received by editor(s) in revised form: July 2, 2019
- Published electronically: September 23, 2019
- Additional Notes: The second author was partially supported by the National Science Foundation Grant No. DMS-1464859.
- Communicated by: Heike Mildenberger
- © Copyright 2019 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 148 (2020), 1283-1293
- MSC (2010): Primary 03E35; Secondary 03E05
- DOI: https://doi.org/10.1090/proc/14771
- MathSciNet review: 4055955