  The main question here is the possible generalization of the following
theorem on ``simple'' equivalence relation on 2^omega to higher cardinals.
  Theorem: (1) Assume that:
  (a) E is a Borel 2-place relation on 2^omega,
  (b) E is an equivalence relation,
  (c) if eta, nu in 2^omega and (exists ! n)(eta(n) not= nu(n)), then eta, nu
are not E --equivalent.
  Then there is a perfect subset of 2^omega of pairwise non E-equivalent
members.
  (2) Instead of ``E is Borel'', ``E is analytic (or even a Borel combination
of analytic relations)'' is enough.
  (3) If E is a Pi^1_2 relation which is an equivalence relation satisfying
clauses (b)+(c) in V^Cohen, then the conclusion of (1) holds.
