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Problem 1170 — Erdős Problems

Problem 1170

Is it consistent that

\omega_2\to (\alpha)_2^2

for every $\alpha <\omega_2$ ?

Source: erdosproblems.com/1170

Set theory
Ramsey theory

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No claim settles this problem.

FoHa03: Foreman, Matthew and Hajnal, Andras, A partition relation for successors of large cardinals. Math. Ann. (2003), 583-623.
La82: Laver, Richard, An $(\aleph \sb{2},\,\aleph \sb{2},\,\aleph \sb{0})$ -saturated ideal on $\omega \sb{1}$ . (1982), 173-180.

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Status: Open
Topics: Set theory
Ramsey theory
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