Automorphisms in the n-generated free algebra in the subvariety of BL-algebras generated by [0, 1]_MV ⊕ [0, 1]_G

BUSANICHE, MANUELA; CASTIGLIONI, JOSÉ LUIS; LUBOMIRSKY, NOEMÍ

Cagliari

Workshop; AsubL (Algebra & Substructural Logics- Take 6); 2018

Università degli studi di Cagliari, Dipartimento di Pedagogia, Psicologia e Filosofia.

In this work we will concentrate in the subvariety MG ⊆ BL generated by the ordinal sum of the algebra [0, 1]_MV and the Gödel hoop [0, 1]_G, that is, generated by A = [0, 1]_MV ⊕ [0, 1]G. Though it is well-known that [0, 1]G is decomposable as an infinite ordinal sum of two-elements Boolean algebra, the idea is to treat it as a whole block. The elements of this block are the dense elements of the generating chain and the elements in [0, 1]_MV are usually called regular elements of A.We study the automorphisms in Free_MG(n). The automorphisms are important since they help us to understand the symmetries of the logic. In the case of the algebra Free_MV(n) the automorphisms are wll known and for the case of the algebra Free_G(n), we give a description based on the one given by Aguzolli, Gerla and Marra for finite Gödel algebras. Using both descriptions, we show a characterization of automorphisms on Free_MG(n).