A theorem in 3-valued model theory with connections to number theory, type theory, and relevant logic
David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
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Studia Logica 38 (2):149 - 169 (1979)
Given classical (2 valued) structures and and a homomorphism h of onto , it is shown how to construct a (non-degenerate) 3-valued counterpart of . Classical sentences that are true in are non-false in . Applications to number theory and type theory (with axiom of infinity) produce finite 3-valued models in which all classically true sentences of these theories are non-false. Connections to relevant logic give absolute consistency proofs for versions of these theories formulated in relevant logic (the proof for number theory was obtained earlier by R. K. Meyer and suggested the present abstract development).
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References found in this work BETA
J. Michael Dunn (1976). Intuitive Semantics for First-Degree Entailments and 'Coupled Trees'. Philosophical Studies 29 (3):149-168.
R. O. Gandy (1956). On the Axiom of Extensionality--Part I. Journal of Symbolic Logic 21 (1):36-48.
R. Routley, R. K. Meyer & L. Goddard (1974). Choice and Descriptions in Enriched Intensional Languages — I. Journal of Philosophical Logic 3 (3):291 - 316.
Citations of this work BETA
R. Routley & R. K. Meyer (1983). Relevant Logics and Their Semantics Remain Viable and Undamaged by Lewis's Equivocation Charge. Topoi 2 (2):205-215.
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