Timeline for If $\kappa \rightarrow (\alpha)^r_2$ holds for every $r\in \omega$, then is $\kappa$ an $\alpha$-Erdős cardinal?
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| May 31, 2013 at 14:25 | comment | added | user33625 |
What about when $\kappa\rightarrow(\alpha)^r_2$ for all $\alpha<\kappa$ and $r<\omega$? I guess it won't make $\kappa \rightarrow (\alpha)^{<\omega}_2$. Though by your answer such a $\kappa$ would be strongly inaccessible since it'd be larger than $\exp_\omega(|\alpha|)$ for every $\alpha<\kappa$. Would $\kappa\rightarrow(\alpha)^2_2$ for all $\alpha<\kappa$ imply $\kappa\rightarrow(\alpha)^r_2$ for all $\alpha<\kappa$ and $r<\omega$?
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| May 31, 2013 at 13:11 | vote | accept | user33625 | ||
| May 31, 2013 at 13:11 | |||||
| May 31, 2013 at 12:58 | history | answered | Péter Komjáth | CC BY-SA 3.0 |