Definition 4.7.3.20. Let $\kappa $ be an infinite cardinal. We say that $\kappa $ is strongly inaccessible if $\kappa = \mathrm{ecf}(\kappa )$. In other words, $\kappa $ is strongly inaccessible if the collection of $\kappa $-small sets is closed under the formation of $\kappa $-small products.
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