Hamel bases and well-ordering the continuum

Authors:
Mariam Beriashvili, Ralf Schindler, Liuzhen Wu and Liang Yu

Journal:
Proc. Amer. Math. Soc.

MSC (2010):
Primary 03E15, 03E20, 03E25

DOI:
https://doi.org/10.1090/proc/14010

Published electronically:
March 9, 2018

Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: In *ZF*, the existence of a Hamel basis does not yield a well-ordering of .

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Schindler, R., Wu, L., and Yu, L.,
*Hamel bases and the principle of dependent choice*, preprint, available at`https://ivv5hpp.uni-muenster.de/u/rds/hamelbasis2.pdf`

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Additional Information

**Mariam Beriashvili**

Affiliation:
Ivane Javakhishvili Tbilisi State University and Ilia Vekua Institute of Applied Mathematics, Tbilisi, Georgia

**Ralf Schindler**

Affiliation:
Institut für Mathematische Logik und Grundlagenforschung, Universität Münster, Einsteinstr. 62, 48149 Münster, Germany

**Liuzhen Wu**

Affiliation:
Institute of Mathematics, Chinese Academy of Sciences, East Zhong Guan Cun Road No. 55, Beijing 100190, People’s Republic of China

**Liang Yu**

Affiliation:
Institute of Mathematical Sciences, Nanjing University, Nanjing, Jiangsu Province 210093, People’s Republic of China

DOI:
https://doi.org/10.1090/proc/14010

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 Dzamonja

Article copyright:
© Copyright 2018
American Mathematical Society