One-step Heyting algebras and hypersequent calculi with the bounded proof property Nick Bezhanishvili, Silvio Ghilardi, Frederik Möllerström Lauridsen Abstract: We introduce a new weakly analytic subformula property (the bounded proof property) of hypersequent calculi for intermediate logics. We define one-step Heyting algebras and establish semantic criteria characterizing the bounded proof property in terms of these algebraic structures. Finally, using these criteria, we provide a number of examples of calculi for intermediate logics with and without the bounded proof property.