  We investigate atomicity of free algebras and various forms of amalgamation
for BL and MV algebras, and also Heyting algebras, though the latter algebras
may not be linearly ordered, so strictly speaking their corresponding
intuitionistic logic does not belong to many valued logic. Generalizing results
of Comer proved in the classical first order case; working out a sheaf duality
on the Zarski topology defined on the prime spectrum of such algebras, we infer
several definability theorems, and obtain a representation theorem for theories
as continuous sections of Sheaves. We also prove an omitting types theorem for
fuzzy logic, and formulate and prove several of its consequences (in classical
model theory) adapted to our case; that has to do with existence and uniqueness
of prime and atomic models.
