Automorphism groups of Lindenbaum algebras of some propositional many-valued logics with locally finite algebraic semantics

We characterize the structure of the automorphism groups of finitely generated free algebras in locally finite varieties constituting the algebraic semantics of well-known many-valued propositional logics, such as Gödel logic and the logic of Gödel hoops, Nilpotent Minimum logic, n-valued Łukasiewicz logic, Drastic product logic. We introduce the subalgebras of automorphism invariant elements of the free algebras, and study their structure in the case of Gödel algebras.