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.

I. Introduction

In this paper we characterize the automorphism groups of finitely generated free algebras in varieties forming the algebraic semantics of some well-known many-valued propositional logics. Further, we introduce the subalgebras of automorphism invariant elements of finitely generated free Gödel algebras.