Finitely generated free Heyting algebras via Birkhoff duality and coalgebra

Details Finitely generated free Heyting algebras via Birkhoff duality and coalgebra Finitely generated free Heyting algebras via Birkhoff duality and coalgebra

2011-02-14

arxiv.org/abs/1102.2828v2

LMCS 7 (2:9) 2011

Computer Science

Logic in Computer Science

Scientific paper

10.2168/LMCS-7(2:9)2011

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.

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