@article{10_14712_1213_7243_2024_009, author = {Fern\'andez, V{\'\i}ctor}, title = {A {Kalm\'ar-style} completeness proof for the logics of the hierarchy ${\mathbb{I}}^n {\mathbb{P}}^k$}, journal = {Commentationes Mathematicae Universitatis Carolinae}, pages = {485--509}, year = {2023}, volume = {64}, number = {4}, doi = {10.14712/1213-7243.2024.009}, mrnumber = {4813799}, zbl = {07953695}, language = {en}, url = {http://geodesic.mathdoc.fr/articles/10.14712/1213-7243.2024.009/} }