%0 Journal Article %A Fernández, Víctor %T A Kalmár-style completeness proof for the logics of the hierarchy ${\mathbb{I}}^n {\mathbb{P}}^k$ %J Commentationes Mathematicae Universitatis Carolinae %D 2023 %P 485-509 %V 64 %N 4 %U http://geodesic.mathdoc.fr/articles/10.14712/1213-7243.2024.009/ %R 10.14712/1213-7243.2024.009 %G en %F 10_14712_1213_7243_2024_009