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arXiv · 1901.01508

Transcendence bases, well-orderings of the reals and the axiom of choice

Haim Horowitz·Saharon Shelah
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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.

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Haim Horowitz, Saharon Shelah. 2019-01-06. Transcendence bases, well-orderings of the reals and the axiom of choice. https://arxiv.org/abs/1901.01508

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