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Let $\mathrm{SP}$ be the set of upper strongly porous at $0$ subsets of ${ℝ}^{+}$ and let $\widehat{I}\left(\mathrm{SP}\right)$ be the intersection of maximal ideals $I\subseteq \mathrm{SP}$. Some characteristic properties of sets $E\in \widehat{I}\left(\mathrm{SP}\right)$ are obtained. We also find a characteristic property of the intersection of all maximal ideals contained in a given set which is closed under subsets. It is shown that the ideal generated by the so-called completely strongly porous at $0$ subsets of ${ℝ}^{+}$ is a proper subideal of $\widehat{I}\left(\mathrm{SP}\right).$ Earlier, completely strongly porous sets and some of their properties were...