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The Calkin algebra is not countably homogeneous


Authors: Ilijas Farah and Ilan Hirshberg
Journal: Proc. Amer. Math. Soc. 144 (2016), 5351-5357
MSC (2010): Primary 03C50, 03C98, 46L05; Secondary 46L40
DOI: https://doi.org/10.1090/proc/13137
Published electronically: May 23, 2016
MathSciNet review: 3556277
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Abstract: We show that the Calkin algebra is not countably homogeneous, in the sense of continuous model theory. We furthermore show that the connected component of the unitary group of the Calkin algebra is not countably homogeneous.


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Additional Information

Ilijas Farah
Affiliation: Department of Mathematics and Statistics, York University, 4700 Keele Street, North York, Ontario, Canada, M3J 1P3
Email: ifarah@yorku.ca

Ilan Hirshberg
Affiliation: Department of Mathematics, Ben Gurion University of the Negev, P.O.B. 653, Be’er, Sheva 84105, Israel
Email: ilan@math.bgu.ac.il

DOI: https://doi.org/10.1090/proc/13137
Received by editor(s): June 14, 2015
Received by editor(s) in revised form: July 9, 2015, January 28, 2016, January 29, 2016, and February 4, 2016
Published electronically: May 23, 2016
Communicated by: Adrian Ioana
Article copyright: © Copyright 2016 American Mathematical Society