Sh:1093

• Horowitz, H., & Shelah, S. (2021). Transcendence bases, well-orderings of the reals and the axiom of choice. Proc. Amer. Math. Soc., 149(2), 851–858.
• Abstract:
We prove that ZF+DC+"there exists a transcendence basis for the reals"+"there is no well-ordering of the reals" is consistent relative to ZFC. This answers a question of Larson and Zapletal.
• Version 2021-12-03 (8p) published version (8p)
Bib entry
@article{Sh:1093,
author = {Horowitz, Haim and Shelah, Saharon},
title = {{Transcendence bases, well-orderings of the reals and the axiom of choice}},
journal = {Proc. Amer. Math. Soc.},
fjournal = {Proceedings of the American Mathematical Society},
volume = {149},
number = {2},
year = {2021},
pages = {851--858},
issn = {0002-9939},
mrnumber = {4198089},
mrclass = {03E25 (03E35 03E40 12F20)},
doi = {10.1090/proc/15242},
note = {\href{https://arxiv.org/abs/1901.01508}{arXiv: 1901.01508}},
arxiv_number = {1901.01508}
}