= Square principle
{title2=$\Box_\kappa$}
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For an infinite <cardinal> $\kappa$, the square principle supplies <club sets> $C_\zeta\subseteq\zeta$ at limit $\zeta<\kappa^+$, with <order type> at most $\kappa$, coherent at limit points: $C_\gamma=C_\zeta\cap\gamma$ whenever $\gamma$ is a limit point of $C_\zeta$. The bound precludes a single <club set> threading the entire sequence. For regular uncountable $\kappa$, coherence together with the weaker-looking size clause $\operatorname{cf}(\zeta)<\kappa\Rightarrow|C_\zeta|<\kappa$ implies the order-type bound. At $\kappa=\omega$, that clause alone is vacuous and cannot replace the bound.
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