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Finitary Extensions of the Nilpotent Minimum Logic and (Almost) Structural Completeness

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Abstract

In this paper we study finitary extensions of the nilpotent minimum logic (NML) or equivalently quasivarieties of NM-algebras. We first study structural completeness of NML, we prove that NML is hereditarily almost structurally complete and moreover NM\(^{-}\), the axiomatic extension of NML given by the axiom \(\lnot (\lnot \varphi ^{2})^{2}\leftrightarrow (\lnot (\lnot \varphi )^{2})^{2}\), is hereditarily structurally complete. We use those results to obtain the full description of the lattice of all quasivarieties of NM-algebras which allow us to characterize and axiomatize all finitary extensions of NML.

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Authors and Affiliations

  1. Facultat de Matemàtiques i Informàtica, Universitat de Barcelona, Gran Via 585, 08007, Barcelona, Spain

    Joan Gispert

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  1. Joan Gispert
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Correspondence to Joan Gispert.

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Presented by Daniele Mundici

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Gispert, J. Finitary Extensions of the Nilpotent Minimum Logic and (Almost) Structural Completeness. Stud Logica 106, 789–808 (2018). https://doi.org/10.1007/s11225-017-9766-4

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  • DOI: https://doi.org/10.1007/s11225-017-9766-4

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