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. arXiv: 1901.01508 DOI: 10.1090/proc/15242 MR: 4198089
• 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.
• published version (8p)

@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}
}