Semantical conditios for the definability of functions and relations

CAMPERCHOLI, MIGUEL; VAGGIONE, DIEGO

ALGEBRA UNIVERSALIS

BIRKHAUSER VERLAG AG

Lugar: BASEL; Año: 2016 vol. 75

0002-5240

Let L be a first order language and let f (resp. R) be a function (resp. relation) symbol not belonging to L. Let S be any of the following sets{finite conjunctions of atomic L-formulas}{positive open L-formulas}{open Horn L-formulas}{open L-formulas}{primitive positive L-formulas}{existential positive L-formulas}{existential Horn L-formulas}{existential L-formulas}.Let K be a class of LU{f}-structures (resp. LU{R}-structures). In this paper we give semantical conditions characterizing when f (resp. R) isdefinable in K by a formula of S.