Transcendence bases, well-orderings of the reals and the axiom of choice
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.
- Pub Date:
- January 2019
- Mathematics - Logic
- We corrected a gap in the proof of Claim 6