Axiomatizability by (A)(E)!-sentences

CAMPERCHOLI, MIGUEL; VAGGIONE, DIEGO

ARCHIVE FOR MATHEMATICAL LOGIC - (Print)

Springer-Verlag

Año: 2011 vol. 50 p. 713 - 725

0933-5846

A (A)(E)!-sentence is a sentence of the form (A)x₁...x_{n}(E)!y₁...y_{m}O(x,y), where O is a quantifier-free formula, and (E)! stands for "there exist unique". We prove that if C is (up to isomorphism) a finite class of finite models then C is axiomatizable by a set of (A)(E)!-sentences if and only if C is closed under isomorphic images, C has the intersection property, and C is closed under fixed-point submodels. This result is employed to characterize the subclasses of finitely generated discriminator varieties axiomatizable by sentences of the form (A)(E)!⋀p=q.