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I investigate the superintuitionistic analogue of the modal logic ofchequered subsets of $\mathbb{R}^\infty$ introduced by van Benthem et al. It isobserved that this logic possesses the disjunction property, contains the Scottaxiom, fails to contain the Kreisel-Putnam axiom and it is a sublogic of theMedvedev logic.

Some notes on the superintuitionistic logic of chequered subsets of $\mathbb{R}^\infty$