Finitely Generated Free MV-Algebras and Their Automorphism Groups

Studia Logica 61 (1):65 - 78 (1998)
Abstract
The MV-algebra $S_{m}^{\omega}$ is obtained from the (m+1)-valued Łukasiewicz chain by adding infinitesimals, in the same way as Chang's algebra is obtained from the two-valued chain. These algebras were introduced by Komori in his study of varieties of MV-algebras. In this paper we describe the finitely generated totally ordered algebras in the variety $\text{MV}_{m}^{\omega}$ generated by $S_{m}^{\omega}$ . This yields an easy description of the free $\text{M}_{m}^{\omega}$ -algebras over one generator. We characterize the automorphism groups of the free MV-algebras over finitely many generators.
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