Geodesic
The selector principle for analytic equivalence relations does not imply the existence of an $A_2$ well ordering of the continuum
Sbornik. Mathematics, Tome 48 (1984) no. 1, pp. 159-172

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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 $A_2$-selector. It is proved that the selector principle is not equivalent to the existence of an $A_2$ 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. 
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     title = {The selector principle for analytic equivalence relations does not imply the existence of an $A_2$ well ordering of the continuum},
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B. L. Budinas. The selector principle for analytic equivalence relations does not imply the existence of an $A_2$ well ordering of the continuum. Sbornik. Mathematics, Tome 48 (1984) no. 1, pp. 159-172. http://geodesic.mathdoc.fr/item/SM_1984_48_1_a7/