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

lmcs:702 - Logical Methods in Computer Science, May 17, 2011, Volume 7, Issue 2
Finitely generated free Heyting algebras via Birkhoff duality and coalgebra

Authors: Bezhanishvili, Nick and Gehrke, Mai

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.


Source : oai:arXiv.org:1102.2828
DOI : 10.2168/LMCS-7(2:9)2011
Volume: Volume 7, Issue 2
Published on: May 17, 2011
Submitted on: October 5, 2010
Keywords: Computer Science - Logic in Computer Science,Mathematics - Logic,F.4.1


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