Let SP be the set of upper strongly porous at 0 subsets of ℝ+ and let Î(SP) be the intersection of maximal ideals I ⊆ SP. Some characteristic properties of sets E ∈ Î(SP) 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 Î(SP). Earlier, completely strongly porous sets and some of their properties were studied in the paper V.Bilet, O.Dovgoshey (2013/2014).