Abstract
"Weak relevant model structures" (wr-ms) are defined on "weak relevant matrices" by generalizing Brady's model structure $${\mathcal{M}_{\rm CL}}$$ built upon Meyer's Crystal matrix CL. It is shown how to falsify in any wr-ms the Generalized Modus Ponens axiom and similar schemes used to derive Curry's Paradox. In the last section of the paper we discuss how to extend this method of falsification to more general schemes that could also be used in deriving Curry's Paradox.
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