Hamel bases and well–ordering the continuum
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- by Mariam Beriashvili, Ralf Schindler, Liuzhen Wu and Liang Yu PDF
- Proc. Amer. Math. Soc. 146 (2018), 3565-3573 Request permission
Abstract:
In ZF, the existence of a Hamel basis does not yield a well–ordering of ${\mathbb R}$.References
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Additional Information
- Mariam Beriashvili
- Affiliation: Ivane Javakhishvili Tbilisi State University and Ilia Vekua Institute of Applied Mathematics, Tbilisi, Georgia
- MR Author ID: 1073204
- Ralf Schindler
- Affiliation: Institut für Mathematische Logik und Grundlagenforschung, Universität Münster, Einsteinstr. 62, 48149 Münster, Germany
- MR Author ID: 344076
- Liuzhen Wu
- Affiliation: Institute of Mathematics, Chinese Academy of Sciences, East Zhong Guan Cun Road No. 55, Beijing 100190, People’s Republic of China
- MR Author ID: 1051075
- Liang Yu
- Affiliation: Institute of Mathematical Sciences, Nanjing University, Nanjing, Jiangsu Province 210093, People’s Republic of China
- MR Author ID: 725077
- Received by editor(s): January 17, 2017
- Received by editor(s) in revised form: November 3, 2017
- Published electronically: March 9, 2018
- Additional Notes: The first author gratefully acknowledges support from the Marianne und Dr. Horst Kiesow-Stiftung, Frankfurt a.M
The second author was partially supported by the SFB 878 “Groups, geometry, and actions” from the DFG (Deutsche Forschungsgemeinschaft).
The third author would like to acknowledge the support through the funding Projects NSFC 11321101 and 11401567.
The fourth author gratefully acknowledges support from the National Natural Science Fund of China, No. 11322112 and 11671196 and from a Humboldt Research Fellowship for Experienced Researchers. - Communicated by: Mirna Dz̆amonja
- © Copyright 2018 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 146 (2018), 3565-3573
- MSC (2010): Primary 03E15, 03E20, 03E25
- DOI: https://doi.org/10.1090/proc/14010
- MathSciNet review: 3803680