Problem 1170

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Statement. Is it consistent that

$$\omega_2\to (\alpha)_2^2$$

for every $\alpha <\omega_2$?

Status. Open.

Source. erdosproblems.com/1170, accessed 2026-09-04. Cite as: T. F. Bloom, Erdős Problem #1170, https://www.erdosproblems.com/1170.

References.

• [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.

Formalization. None recorded.

Progress

Not yet compiled.

Known Results

Not yet compiled.

Linked library material

These entries are derived from explicit links on library pages. They are navigation only and do not by themselves record mathematical progress.

• erdos_1974_unsolved_solved_problems_set_theory
• erdos_1974_unsolved_solved_problems_set_theory / question_p272
• komjath_2025_erdos_hajnal_problem_list