Abstract
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 Łoś-Tarski and Chang-Łoś-Suszko, Craig-Robinson and the Beth definability theorem.
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References
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Alves, E.H. Paraconsistent logic and model theory. Stud Logica 43, 17–32 (1984). https://doi.org/10.1007/BF00935737
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DOI: https://doi.org/10.1007/BF00935737