999 research outputs found
On the geometric theory of local MV-algebras
We investigate the geometric theory of local MV-algebras and its quotients
axiomatizing the local MV-algebras in a given proper variety of MV-algebras. We
show that, whilst the theory of local MV-algebras is not of presheaf type, each
of these quotients is a theory of presheaf type which is Morita-equivalent to
an expansion of the theory of lattice-ordered abelian groups. Di
Nola-Lettieri's equivalence is recovered from the Morita-equivalence for the
quotient axiomatizing the local MV-algebras in Chang's variety, that is, the
perfect MV-algebras. We establish along the way a number of results of
independent interest, including a constructive treatment of the radical for
MV-algebras in a fixed proper variety of MV-algebras and a representation
theorem for the finitely presentable algebras in such a variety as finite
products of local MV-algebras.Comment: 52 page
Fields and Fusions: Hrushovski constructions and their definable groups
An overview is given of the various expansions of fields and fusions of
strongly minimal sets obtained by means of Hrushovski's amalgamation method, as
well as a characterization of the groups definable in these structures
- …