Notes on the Model Theory of DeMorgan Logics

Notre Dame Journal of Formal Logic 53 (1):113-132 (2012)
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Abstract

We here make preliminary investigations into the model theory of DeMorgan logics. We demonstrate that Łoś's Theorem holds with respect to these logics and make some remarks about standard model-theoretic properties in such contexts. More concretely, as a case study we examine the fate of Cantor's Theorem that the classical theory of dense linear orderings without endpoints is $\aleph_{0}$-categorical, and we show that the taking of ultraproducts commutes with respect to previously established methods of constructing nonclassical structures, namely, Priest's Collapsing Lemma and Dunn's Theorem in 3-Valued Logic

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Thomas Ferguson
City University of New York

References found in this work

Saving truth from paradox.Hartry H. Field - 2008 - New York: Oxford University Press.
Minimally inconsistent LP.Graham Priest - 1991 - Studia Logica 50 (2):321 - 331.
Inconsistent models of artihmetic Part II : The general case.Graham Priest - 2000 - Journal of Symbolic Logic 65 (4):1519-1529.
A Note on Priest's Finite Inconsistent Arithmetics.J. B. Paris & N. Pathmanathan - 2006 - Journal of Philosophical Logic 35 (5):529-537.

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