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A Note on Natural Extensions in Abstract Algebraic Logic

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Abstract

Transfer theorems are central results in abstract algebraic logic that allow to generalize properties of the lattice of theories of a logic to any algebraic model and its lattice of filters. Their proofs sometimes require the existence of a natural extension of the logic to a bigger set of variables. Constructions of such extensions have been proposed in particular settings in the literature. In this paper we show that these constructions need not always work and propose a wider setting (including all finitary logics and those with countable language) in which they can still be used.

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Authors and Affiliations

  1. Institute of Computer Science, Academy of Sciences of the Czech Republic, Pod vodárenskou věží 2, 182 07, Prague, Czech Republic

    Petr Cintula

  2. Institute of Information Theory and Automation, Academy of Sciences of the Czech Republic, Pod vodárenskou věží 4, 182 08, Prague, Czech Republic

    Carles Noguera

Authors
  1. Petr Cintula
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  2. Carles Noguera
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Correspondence to Carles Noguera.

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Presented by Jacek Malinowski

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Cintula, P., Noguera, C. A Note on Natural Extensions in Abstract Algebraic Logic. Stud Logica 103, 815–823 (2015). https://doi.org/10.1007/s11225-014-9594-8

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  • DOI: https://doi.org/10.1007/s11225-014-9594-8

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