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- Title
Involutive symmetric Gödel spaces, their algebraic duals and logic.
- Authors
Di Nola, A.; Grigolia, R.; Vitale, G.
- Abstract
It is introduced a new algebra (A , ⊗ , ⊕ , ∗ , ⇀ , 0 , 1) called L P G -algebra if (A , ⊗ , ⊕ , ∗ , 0 , 1) is L P -algebra (i.e. an algebra from the variety generated by perfect MV-algebras) and (A , ⇀ , 0 , 1) is a Gödel algebra (i.e. Heyting algebra satisfying the identity (x ⇀ y) ∨ (y ⇀ x) = 1) . The lattice of congruences of an L P G -algebra (A , ⊗ , ⊕ , ∗ , ⇀ , 0 , 1) is isomorphic to the lattice of Skolem filters (i.e. special type of MV-filters) of the MV-algebra (A , ⊗ , ⊕ , ∗ , 0 , 1) . The variety L P G of L P G -algebras is generated by the algebras (C , ⊗ , ⊕ , ∗ , ⇀ , 0 , 1) where (C , ⊗ , ⊕ , ∗ , 0 , 1) is Chang MV-algebra. Any L P G -algebra is bi-Heyting algebra. The set of theorems of the logic L P G is recursively enumerable. Moreover, we describe finitely generated free L P G -algebras.
- Subjects
ALGEBRAIC logic; SYMMETRIC spaces; HEYTING algebras; VARIETIES (Universal algebra); ALGEBRAIC varieties; CONGRUENCE lattices
- Publication
Archive for Mathematical Logic, 2023, Vol 62, Issue 5/6, p789
- ISSN
0933-5846
- Publication type
Article
- DOI
10.1007/s00153-023-00866-6