Borel rectangles

by Shelah. [Sh:532]

We prove the consistency of the existence of co- aleph_1-Souslin equivalence relation on {}^omega 2 with any pregiven aleph_alpha class, alpha < omega_1 but not a perfect set of pairwise non-equivalent. We deal also with co- kappa-Souslin relations, equivalence relations, exact characterizations and Pi^1_2-equivalence relations and rectangles. To 666: problem on equalities of x 's; deal with co- kappa-Souslin deal with the k-notation and the alpha-notation. 2012.8.16 In Poland - July- has written a new try, in order to get a Borel relation with aleph_alpha rectangle but no more, for any countable ordinal alpha . What was written was only the forcing. Yesterday, proofread it, expand - still has to write kappa-Delta pair proof, and thoughts about more than aleph_y w_1 But the rank in [522, section 4] seem not OK, will try to revise


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