The classical model existence theorem in subclassical predicate logics I
pp. 187-199
in: David Makinson, Jacek Malinowski, Heinrich Wansing (eds), Towards mathematical philosophy, Berlin, Springer, 2009Abstract
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.