Erdős Problem #1171

Is it true that, for all finite $k<\omega$,\[\omega_1^2\to (\omega_1\omega, 3,\ldots,3)_{k+1}^2?\]

set theory | ramsey theory

Disclaimer: The open status of this problem reflects the current belief of the owner of this website. There may be literature on this problem that I am unaware of, which may partially or completely solve the stated problem. Please do your own literature search before expending significant effort on solving this problem. If you find any relevant literature not mentioned here, please add this in a comment.

Baumgartner [Ba89b] proved that, assuming a form of Martin's axiom, that $\omega_1\omega\to (\omega_1\omega, 3)^2$.

View the LaTeX source

This page was last edited 26 January 2026.

External data from the database - you can help update this
Formalised statement? No (Create a formalisation here)

0 comments on this problem

Likes this problem	None
Interested in collaborating	None
Currently working on this problem	None
This problem looks difficult	None
This problem looks tractable	None
The results on this problem could be formalisable	None
I am working on formalising the results on this problem	None

When referring to this problem, please use the original sources of Erdős. If you wish to acknowledge this website, the recommended citation format is:

T. F. Bloom, Erdős Problem #1171, https://www.erdosproblems.com/1171, accessed 2026-03-01