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

Haim Horowitz; Saharon Shelah

doi:10.1090/proc/15242

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

Haim Horowitz, Saharon Shelah

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

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.

Original language	English
Pages (from-to)	851-858
Number of pages	8
Journal	Proceedings of the American Mathematical Society
Volume	149
Issue number	2
DOIs	https://doi.org/10.1090/proc/15242
State	Published - Feb 2021
Externally published	Yes

Bibliographical note

Publisher Copyright:
© 2020 American Mathematical Society

Keywords

Amalgamation
Axiom of choice
Forcing
Transcendence basis
Well-ordering

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10.1090/proc/15242

Cite this

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KW - Forcing

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KW - Well-ordering

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

Abstract

Bibliographical note

Keywords

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