A theorem in 3-valued model theory with connections to number theory, type theory, and relevant logic

Studia Logica 38 (2):149 - 169 (1979)
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Abstract

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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Author's Profile

Jon Michael Dunn
PhD: University of Pittsburgh; Last affiliation: Indiana University, Bloomington

Citations of this work

Partiality and its dual.J. Michael Dunn - 2000 - Studia Logica 66 (1):5-40.
Wittgenstein on Incompleteness Makes Paraconsistent Sense.Francesco Berto - 2008 - In Francesco Berto, Edwin Mares, Koji Tanaka & Francesco Paoli (eds.), Paraconsistency: Logic and Applications. Springer. pp. 257--276.
Notes on the Model Theory of DeMorgan Logics.Thomas Macaulay Ferguson - 2012 - Notre Dame Journal of Formal Logic 53 (1):113-132.
Relevant Robinson's arithmetic.J. Michael Dunn - 1979 - Studia Logica 38 (4):407 - 418.

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References found in this work

Completeness of relevant quantification theories.Robert K. Meyer, J. Michael Dunn & Hugues Leblanc - 1974 - Notre Dame Journal of Formal Logic 15 (1):97-121.
New axiomatics for relevant logics, I.Robert K. Meyer - 1974 - Journal of Philosophical Logic 3 (1/2):53 - 86.
On the axiom of extensionality – Part I.R. O. Gandy - 1956 - Journal of Symbolic Logic 21 (1):36-48.

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