The Classical Model Existence Theorem in Subclassical Predicate Logics I
We prove that in predicate logics there are some classically sound Hilbert systems which satisfy the classical model existence theorem (every ⊥-consistent set has a classical model) but are weaker than first order logic.
Keywordsextended completeness theorem strong completeness prenex normal form intuitionistic logic three-valued logic
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- Hunter, G., Metalogic. An Introduction to the Metatheory of Standard First Order Logic, University of California Press, 1973. Google Scholar
- Lee, J.-L., ‘On Gödel’s Completeness Theorem’, presented in 12th International Congress of Logic Methodology and Philosophy of Science, at Oviedo, Spain, August 2003. Google Scholar
- Lee, J.-L., ‘Classical model existence theorem in propositional logics’, in Béziau, Jean-Yves, Costa-Leite, Alexandre (eds.), Perspectives on Universal Logic, Polimetrica, Monza, Italy, 2007, pp. 179–197. Google Scholar
- Lee, J.-L., Classical model existence and resolution, manuscript, 2007. Google Scholar
- Shapiro, S., ‘Classical logic II: Higher-order logic’, in Goble, L. (ed.), The Blackwell Guide to Philosophical Logic, Blackwell Publishers Ltd., 2001, pp. 33–54. Google Scholar
- Sundholm, G., ‘Systems of deduction’, in Gabbay, D.M., Guenthner, F. (eds.), Handbook of Philosophical Logic, vol. 2, Kluwer Acad. Publ., Dordrecht, 2001, pp. 1–52. Google Scholar