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

Matteo Bianchi

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arXiv · 1103.5943

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

Matteo Bianchi

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Abstract

We present the logic BL_Chang, an axiomatic extension of BL (see P. Hájek - 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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BibTeX RIS

Matteo Bianchi. 2012-04-04. The variety generated by all the ordinal sums of perfect MV-chains. https://arxiv.org/abs/1103.5943

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