### On $CH + 2^{\aleph_1}\rightarrow(\alpha)^2_2$ for $\alpha<\omega_2$

by Shelah. [Sh:424]

Logic Colloquium'90. ASL Summer Meeting in Helsinki, 1993

We prove the consistency of ``CH + 2^{aleph_1} is
arbitrarily large +
2^{aleph_1} not-> (omega_1 x omega)^2_2''. If fact,
we can get
2^{aleph_1} not-> [omega_1 x omega]^2_{aleph_0} . In
addition to this theorem, we give generalizations to other
cardinals.

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