Square and stationary reflection - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-25T04:58:46Z http://mathoverflow.net/feeds/question/105655 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/105655/square-and-stationary-reflection Square and stationary reflection Chris Lambie-Hanson 2012-08-27T20:10:33Z 2012-08-27T20:10:33Z <p>It is easily shown that, for any uncountable infinite cardinal $\kappa$, $\square_\kappa$ implies that for any stationary $S\subseteq \kappa^+$, there exists a stationary $T\subseteq S$ such that $T$ does not reflect at (i.e. is not stationary in) any $\alpha&lt;\kappa$ of uncountable cofinality. The standard proof does not go through, however, when $\square_\kappa$ is replaced by the weaker notion of $\square(\kappa^+)$. Is $\square(\kappa^+)$ compatible with stationary reflection? More precisely, if $\kappa$ is an uncountable infinite cardinal, is $\square(\kappa^+)$ consistent with the statement "every stationary $S\subseteq \kappa^+$ consisting of ordinals of cofinality $&lt;\kappa$ reflects at some $\alpha&lt;\kappa^+$"?</p>