= Non-reflecting subset
{title2=$\{\delta<\lambda:\operatorname{cf}(\delta)>\omega,\ X\cap\delta\text{ stationary in }\delta\}=\varnothing$}
A <subset> $X\subseteq\lambda$ is non-reflecting in the indicated sense if it is not stationary below any $\delta<\lambda$ of uncountable <cofinality>. The <subset> itself need not be stationary. Nonreflection is inherited by <subsets>. With this definition every <subset> of $\omega_1$ is non-reflecting, since all smaller <ordinals> have countable <cofinality>.
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