Spectra of Gödel Algebras.
TbiLLC(2018)
摘要
We exploit the duality between finite Gödel algebras and their homomorphisms, and the category of finite forests and open maps, to compute the duals of non-isomorphic k -element Gödel algebras, for . From this construction we obtain a recurrence formula to compute the fine spectrum of the variety of Gödel algebras . Using such a formula we easily compute the set of cardinalities of finite Gödel algebras (the spectrum of ), that is equal to the set of positive integers . To complete the picture on spectra of Gödel algebras, we recall the well-known recurrence formula to compute the cardinality of every free k -generated Gödel algebra, that is the free spectrum of .
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