Hamel bases and well–ordering the continuum
نویسندگان
چکیده
منابع مشابه
Hamel bases and well–ordering the continuum
In ZF, the existence of a Hamel basis does not yield a well–ordering of R. Throughout this paper, by a Hamel basis we always mean a basis for R, construed as a vector space over Q. We denote by E the Vitali equivalence relation, xEy iff x− y ∈ Q for x, y ∈ R. We also write [x]E = {y : yEx} for the E–equivalence class of x. A transversal for the set of all E–equivalence classes picks exactly one...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 2018
ISSN: 0002-9939,1088-6826
DOI: 10.1090/proc/14010