Transcendence bases, well-orderings of the reals and the axiom of choice. Horowitz, H. & Shelah, S. Archive for Mathematical Logic. arxiv:math/1901.01508
bibtex   
@article{HwSh:1093,
author = {Horowitz, Haim and Shelah, Saharon},
trueauthor = {Horowitz, Haim and Shelah, Saharon},
fromwhere = {IL,IL},
journal = {Archive for Mathematical Logic},
note = { arxiv:math/1901.01508 },
title = {{Transcendence bases, well-orderings of the reals and the	axiom
 of choice}},
volume = {old title has become a part of 1090 which appeared in AML},
}
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