Ideals, Cohen sets and consistent extensions of the Erdős-Dushnik-Miller Theorem
Saharon Shelah, Lee Stanley
Abstract
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, alephomega1 not-> (alephomega1, omega+1)2 and consistently, 2aleph0 not-> (2aleph0,omega +1)2 .
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