On the variety of Gödel MV-algebras

Abstract

We introduce a new algebraic structure $$\begin{aligned} (A, \otimes , \oplus , *, \vee , \wedge , \rightharpoonup , 0, 1) \end{aligned}$$ called Godel–MV-algebra (GMV-algebra) such that It is shown that the lattice of congruences of a GMV -algebra $$(A, \otimes , \oplus , *, \rightharpoonup , 0, 1)$$ is isomorphic to the lattice of Skolem filters (i. e. special type of MV-filters) of the MV-algebra $$(A, \otimes , \oplus , *, 0, 1)$$ . Any GMV-algebra is bi-Heyting algebra. Any chain GMV-algebra is simple, and any GMV-algebra is semi-simple. Finitely generated GMV-algebras are described, and finitely generated finitely presented GMV-algebras are characterized. The algebraic counterpart of axiomatically presented GMV-logic is GMV-algebras .