## Abstract

We introduce a new algebraic structure called It is shown that the lattice of congruences of a

$$\begin{aligned} (A, \otimes , \oplus , *, \vee , \wedge , \rightharpoonup , 0, 1) \end{aligned}$$

*Gödel*–*MV-algebra*(*GMV*-*algebra*) such that-
\((A, \otimes , \oplus , *, 0, 1)\) is

*MV*-algebra; -
\((A,\vee , \wedge ,\rightharpoonup , 0, 1)\) is a Gödel algebra (i. e. Heyting algebra satisfying the identity \((x \rightharpoonup y ) \vee (y \rightharpoonup x ) =1\)).

*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 .## Keywords

*MV*-algebra Gödel algebra Many-valued logic

## Notes

### Compliance with ethical standards

### Conflict of interest

Authors declare that they have no conflict of interest.

### Ethical approval

This article does not contain any studies with human participants or animals performed by any of the authors.

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