Transcendence bases, well-orderings of the reals and the axiom of choice
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.
- Publication:
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arXiv e-prints
- Pub Date:
- January 2019
- DOI:
- 10.48550/arXiv.1901.01508
- arXiv:
- arXiv:1901.01508
- Bibcode:
- 2019arXiv190101508H
- Keywords:
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- Mathematics - Logic
- E-Print:
- We corrected a gap in the proof of Claim 6