Abstract:
A set is called a selector of an equivalence relation defined on all the real numbers if it intersects each equivalence class of this relation in a singleton set. The following proposition is called the selector principle: each analytic equivalence relation on the set of all real numbers has an A2-selector. It is proved that the selector principle is not equivalent to the existence of an A2 well ordering of the continuum. This answers a question posed by Burgess. Equivalence is understood in the sense of equivalence in the standard Zermelo–Fraenkel set theory with the axiom of choice.
Bibliography: 8 titles.
Citation:
B. L. Budinas, “The selector principle for analytic equivalence relations does not imply the existence of an A2 well ordering of the continuum”, Math. USSR-Sb., 48:1 (1984), 159–172
\Bibitem{Bud83}
\by B.~L.~Budinas
\paper The selector principle for analytic equivalence relations does not imply the existence of an $A_2$ well ordering of the continuum
\jour Math. USSR-Sb.
\yr 1984
\vol 48
\issue 1
\pages 159--172
\mathnet{http://mi.mathnet.ru/eng/sm2113}
\crossref{https://doi.org/10.1070/SM1984v048n01ABEH002666}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=687609}
\zmath{https://zbmath.org/?q=an:0563.03031}
Linking options:
https://www.mathnet.ru/eng/sm2113
https://doi.org/10.1070/SM1984v048n01ABEH002666
https://www.mathnet.ru/eng/sm/v162/i2/p164
This publication is cited in the following 1 articles:
V. G. Kanovei, “The development of the descriptive theory of sets under the influence of the work of Luzin”, Russian Math. Surveys, 40:3 (1985), 135–180
Citation in format AMSBIB
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