Nick Bezhanishvili ; Mai Gehrke - Finitely generated free Heyting algebras via Birkhoff duality and coalgebra

lmcs:702 - Logical Methods in Computer Science, May 17, 2011, Volume 7, Issue 2 - https://doi.org/10.2168/LMCS-7(2:9)2011
Finitely generated free Heyting algebras via Birkhoff duality and coalgebraArticle

Authors: Nick Bezhanishvili ORCID; Mai Gehrke

    Algebras axiomatized entirely by rank 1 axioms are algebras for a functor and thus the free algebras can be obtained by a direct limit process. Dually, the final coalgebras can be obtained by an inverse limit process. In order to explore the limits of this method we look at Heyting algebras which have mixed rank 0-1 axiomatizations. We will see that Heyting algebras are special in that they are almost rank 1 axiomatized and can be handled by a slight variant of the rank 1 coalgebraic methods.


    Volume: Volume 7, Issue 2
    Published on: May 17, 2011
    Imported on: October 5, 2010
    Keywords: Computer Science - Logic in Computer Science,Mathematics - Logic,F.4.1
    Funding:
      Source : OpenAIRE Graph
    • Relational Semantics for Substructural and Other Logics; Funder: UK Research and Innovation; Code: EP/E029329/1
    • Order-topological and model-theoretic methods for modal logics; Funder: UK Research and Innovation; Code: EP/F032102/1

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