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The Variety Generated by all the Ordinal Sums of Perfect MV-Chains

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Abstract

We present the logic BLChang, an axiomatic extension of BL (see [23]) 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 BLChang-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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  1. Dipartimento di Informatica e Comunicazione, Università degli Studi di Milano, via comelico 39/41, 20135, Milan, Italy

    Matteo Bianchi

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Correspondence to Matteo Bianchi.

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Dedicated to my friend Erika, and to her invaluable talent in finding surprisingly deep connections among poetry, art, philosophy and logic.

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Bianchi, M. The Variety Generated by all the Ordinal Sums of Perfect MV-Chains. Stud Logica 101, 11–29 (2013). https://doi.org/10.1007/s11225-012-9371-5

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