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Borel partitions of infinite subtrees of a perfect tree
[article]
1993
arXiv
pre-print
A theorem of Galvin asserts that if the unordered pairs of reals are partitioned into finitely many Borel classes then there is a perfect set P such that all pairs from P lie in the same class. The generalization to n-tuples for n >= 3 is false. Let us identify the reals with 2^omega ordered by the lexicographical ordering and define for distinct x,y in 2^omega, D(x,y) to be the least n such that x(n) not= y(n). Let the type of an increasing n-tuple x_0, ... x_n-1_< be the ordering <^* on 0,
arXiv:math/9301209v1
fatcat:hj76wbl7brfcdi7jz6qfq5jfeq