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