Skolemization in intermediate logics with the finite model property

An alternative Skolemization method, which removes strong quantifiers from formulas, is presented that is sound and complete with respect to intermediate predicate logics with the finite model property. For logics without constant domains the method makes use of an existence predicate, while for logics with constant domains no additional predicate is necessary. In both cases, an analogue of Hebrand's theorem is obtained and it is proved that the one-variable fragment of a logic with the finite model property is decidable once the propositional fragment of the logic is. It is also shown that universal constant domain logics with the finite model property have interpolation once their propositional fragment has. For logics without constant domains some of these results, but with far more complicated proofs, have been obtained by the second author in the paper The eskolemization of universal quantiers. Annals of Pure and Applied Logic, 162(3): 201–212 (2010).