Abstract
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.
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Lee, JL. (2009). The Classical Model Existence Theorem in Subclassical Predicate Logics I. In: Makinson, D., Malinowski, J., Wansing, H. (eds) Towards Mathematical Philosophy. Trends in Logic, vol 28. Springer, Dordrecht. https://doi.org/10.1007/978-1-4020-9084-4_9
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DOI: https://doi.org/10.1007/978-1-4020-9084-4_9
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