Logics to which the class of neat reducts is sensitive to

Abstract

Let L be a quantifier predicate logic. Let K be a class of algebras. We say that K is sensitive to L, if there is an algebra in K, that is L interpretable into an another algebra, and this latter algebra is elementary equivalent to an algebra not in K. (In particular, if L is L_{\omega,\omega}, this means that K is not elementary). We show that the class of neat reducts of every dimension is sensitive to quantifier free predicate logics with infinitary conjunctions; for finite dimensions, we do not need infinite conjunctions.