Geodesic
A~Cofinal Family of Equivalence Relations and Borel Ideals Generating Them
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Geometric topology, discrete geometry, and set theory, Tome 252 (2006), pp. 94-113

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An increasing $\omega _1$-sequence of Borel equivalence relations on a Polish space that is cofinal (in the sense of Borel reducibility) in the family of all Borel equivalence relations is defined as a development of Rosendal's construction. It is proved that equivalence relations from this sequence are generated by explicitly defined Borel ideals. 
@article{TM_2006_252_a9,
     author = {V. G. Kanovei and V. A. Lyubetskii},
     title = {A~Cofinal {Family} of {Equivalence} {Relations} and {Borel} {Ideals} {Generating} {Them}},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {94--113},
     publisher = {mathdoc},
     volume = {252},
     year = {2006},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TM_2006_252_a9/}
}
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V. G. Kanovei; V. A. Lyubetskii. A~Cofinal Family of Equivalence Relations and Borel Ideals Generating Them. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Geometric topology, discrete geometry, and set theory, Tome 252 (2006), pp. 94-113. http://geodesic.mathdoc.fr/item/TM_2006_252_a9/