Paraconsistent logic and model theory

Studia Logica 43 (1-2):17 - 32 (1984)
The object of this paper is to show how one is able to construct a paraconsistent theory of models that reflects much of the classical one. In other words the aim is to demonstrate that there is a very smooth and natural transition from the model theory of classical logic to that of certain categories of paraconsistent logic. To this end we take an extension of da Costa''sC 1 = (obtained by adding the axiom A A) and prove for it results which correspond to many major classical model theories, taken from Shoenfield [5]. In particular we prove counterparts of the theorems of o-Tarski and Chang-o-Suszko, Craig-Robinson and the Beth definability theorem
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DOI 10.1007/BF00935737
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Joseph R. Shoenfield (1967). Mathematical Logic. Reading, Mass.,Addison-Wesley Pub. Co..

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