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Rings and Modules Seminar
~ Abstracts ~

Julian Salamanca Tellez, University of Manitoba
salamanj(at)myumanitoba(dot)ca

Department of Mathematics
University of Manitoba

Tuesday, April 08, 2014

A Characterization of Compatible Functions in Distributive Lattices
Abstract:

Two characterizations for compatible functions on Heyting algebras are shown in [1], one of those characterizations does not include the implication operation of a Heyting algebra and it only includes the meet lattice operation. That raises the question whether we can replace "Heyting algebra" by "distributive lattice" in that case or not. I will show that this is not the case, but a similar characterization for compatible functions on distributive lattices will be shown. As an application, using that result we can show how implicitly defined operations, as they are defined in [2], behave on distributive lattices.

References:
  1. X. Caicedo and R. Cignoli, An Algebraic Approach to Intuitionistic Connectives, The Journal of Symbolic Logic 66 (2001), 1620–1636.
  2. J. Reiterman, The Birkhoff Theorem for Finite Algebras, Algebra Universalis 14 (1982), 1–10.

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