Definable Hamel bases and ${\sf AC}_\omega ({\mathbb R})$
Volume 253 / 2021
Fundamenta Mathematicae 253 (2021), 239-256
MSC: Primary 03E15; Secondary 03E35.
DOI: 10.4064/fm909-6-2020
Published online: 17 December 2020
Abstract
There is a model of ${\sf ZF}$ with a lightface $\Delta ^1_3$ definable Hamel bases in which ${\sf AC}_\omega ({\mathbb R})$ fails.
