Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

A note on the eightfold way


Authors: Thomas Gilton and John Krueger
Journal: Proc. Amer. Math. Soc. 148 (2020), 1283-1293
MSC (2010): Primary 03E35; Secondary 03E05
DOI: https://doi.org/10.1090/proc/14771
Published electronically: September 23, 2019
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2010): 03E35, 03E05

Retrieve articles in all journals with MSC (2010): 03E35, 03E05


Additional Information

Thomas Gilton
Affiliation: Department of Mathematics, University of California, Los Angeles, Box 951555, Los Angeles, California 90095-1555
Email: tdgilton@math.ucla.edu

John Krueger
Affiliation: Department of Mathematics, University of North Texas, 1155 Union Circle #311430, Denton, Texas 76203
Email: jkrueger@unt.edu

DOI: https://doi.org/10.1090/proc/14771
Keywords: Stationary reflection, Aronszajn tree, approachability property, disjoint stationary sequence
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
Article copyright: © Copyright 2019 American Mathematical Society