### Filters, Cohen Sets and Consistent Extensions of the Erd\H{o}s-Dushnik-Miller Theorem

by Shelah and Stanley. [ShSt:419]

J Symbolic Logic, 2000

We present two different types of models where, for certain
singular cardinals lambda of uncountable cofinality, lambda->
(lambda, omega +1)^2, although lambda is not
a strong limit cardinal. We announce, here, and will present
in a
subsequent paper, that, for example, consistently, aleph_{omega_1}
not-> (aleph_{omega_1}, omega +1)^2
and consistently, 2^{aleph_0} not-> (2^{aleph_0}, omega +1)^2 .

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