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Transcendence bases, well-orderings of the reals and the axiom of choice
Proceedings of the American Mathematical Society ( IF 1 ) Pub Date : 2020-12-16 , DOI: 10.1090/proc/15242
Haim Horowitz , Saharon Shelah

Abstract:We prove that $ ZF\!+\!DC\!+$$ \text {\lq\lq there exists a transcendence basis for the reals''}\linebreak +\text {\lq\lq there is no well-ordering of the reals''}$ is consistent relative to $ ZFC$. This answers a question of Larson and Zapletal.


中文翻译:

超越基础,实物的有序排列和选择公理

摘要:我们证明相对于是一致的。这回答了拉森和扎普勒塔尔的问题。 $ ZF \!+ \!DC \!+ $$ \ text {\ lq \ lq存在对实数的超越依据”} \ linebreak + \ text {\ lq \ lq没有对实数的良好排序”} $$ ZFC $
更新日期:2021-01-11
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