Translating open formulas

CAMPERCHOLI, MIGUEL

Pucón

Congreso; XIX Coloquio Latinoamericano de Álgebra; 2012

The quaternary discriminator on a set A is the function defined by d(x,y,z,w)=z if x=y and d(x,y,z,w)=w if x!=y Let L be a first order language without relations, and let K be a class of L-models. It is well known that if there is an L- term representing the quaternary discriminator in every member of K then: (T) every trivially satisfiable open formula is equivalent to a conjunction of equations over K. This translation property is one of several strong consequences of the presence of a discriminator term in the class K. However, it is not sufficient to imply the existence of such a term. In our talk we shall see that (T) is in fact equivalent (among other conditions) to the quaternary discriminator being definable in K by a conjunction of equations. The results in this talk are joint work with Diego Vaggione.