Generalized Medvedev logics from topless finite rooted frame products are not finitely axiomatizable; at least countably many exist and none is least.
Some notes on the superintuitionistic logic of chequered subsets of $\mathbb{R}^\infty$
1 Pith paper cite this work. Polarity classification is still indexing.
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abstract
I investigate the superintuitionistic analogue of the modal logic of chequered subsets of $\mathbb{R}^\infty$ introduced by van Benthem et al. It is observed that this logic possesses the disjunction property, contains the Scott axiom, fails to contain the Kreisel-Putnam axiom and it is a sublogic of the Medvedev logic.
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2026 1verdicts
UNVERDICTED 1representative citing papers
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Non-finite Axiomatizability of Generalized Medvedev Logics
Generalized Medvedev logics from topless finite rooted frame products are not finitely axiomatizable; at least countably many exist and none is least.