Title of article
Gِdel algebras free over finite distributive lattices
Author/Authors
Aguzzoli، نويسنده , , Stefano and Gerla، نويسنده , , Brunella and Marra، نويسنده , , Vincenzo، نويسنده ,
Issue Information
روزنامه با شماره پیاپی سال 2008
Pages
11
From page
183
To page
193
Abstract
Gödel algebras form the locally finite variety of Heyting algebras satisfying the prelinearity axiom ( x → y ) ∨ ( y → x ) = ⊤ . In 1969, Horn proved that a Heyting algebra is a Gödel algebra if and only if its set of prime filters partially ordered by reverse inclusion–i.e. its prime spectrum–is a forest. Our main result characterizes Gödel algebras that are free over some finite distributive lattice by an intrisic property of their spectral forest.
Keywords
Heyting algebras , Distributive lattices , Free objects , 06D20 , Duality for finitely presented objects , 06D50 , Partially Ordered Sets , Gِdel algebras
Journal title
Annals of Pure and Applied Logic
Serial Year
2008
Journal title
Annals of Pure and Applied Logic
Record number
1444261
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