  MV-algebras are an algebraic semantics for Lukasiewicz logic and MV-algebras
generated by a finite chain are Heyting algebras where the Godel implication
can be written in terms of De Morgan and Moisil's modal operators. In our work,
a fragment of trivalent Lukasiewicz logic is studied. The propositional and
first-order logic is presented. The maximal consistent theories are studied as
Monteiro's maximal deductive systems of the Lindenbaum-Tarski algebra, in both
cases. Consequently, the adequacy theorem with respect to the suitable
algebraic structures is proven.
