The variety generated by all the ordinal sums of perfect MV-chains

Details The variety generated by all the ordinal sums of perfect MV-chains The variety generated by all the ordinal sums of perfect MV-chains

2011-03-30

arxiv.org/abs/1103.5943v2

Mathematics

Logic

This is a revised version of the previous paper: the modifications concern essentially the presentation. The scientific conten

Scientific paper

We present the logic BL_Chang, an axiomatic extension of BL (see P. H\'ajek - Metamathematics of fuzzy logic - 1998, Kluwer) whose corresponding algebras form the smallest variety containing all the ordinal sums of perfect MV-chains. We will analyze this logic and the corresponding algebraic semantics in the propositional and in the first-order case. As we will see, moreover, the variety of BL_Chang-algebras will be strictly connected to the one generated by Chang's MV-algebra (that is, the variety generated by all the perfect MV-algebras): we will also give some new results concerning these last structures and their logic.

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