Problem 70

Erdős Problem #70: declared status 'open'. Formalized: no. Let $\mathfrak{c}$ be the ordinal of the real numbers, $\beta$ be any countable ordinal, and $2\leq n<\omega$. Is it true that $\mathfrak{c}\to (\beta, n)_2^3$? Current best: Erd\H{o}s and Rado proved that $\mathfrak{c}\to (\omega+n,4)_2^3$ for any $2\leq n<\omega$. Prize: no. Tags: graph theory, ramsey theory, set theory.