The category of Gödel spaces GS (with strongly isotone maps as morphisms), which are dually equivalent to the category of Gödel algebras, is transferred by a contravariant functor H into the category MV(C)<sup>G</sup> of MV-algebras generated by perfect MV-chains via the operators of direct products, subalgebras and direct limits. Conversely, the category MV(C)<sup>G</sup> is transferred into the category GS by means of a contravariant functor P. Moreover, it is shown that the functor H is faithful, the functor P is full and the both functors are dense. The description of finite coproduct of algebras, which are isomorphic to Chang algebra, is given. Using duality a characterization of projective algebras in MV(C)<sup>G</sup> is given.

Gödel spaces and perfect MV-algebras

DI NOLA, Antonio;GRIGOLIA , REVAZ
2015-01-01

Abstract

The category of Gödel spaces GS (with strongly isotone maps as morphisms), which are dually equivalent to the category of Gödel algebras, is transferred by a contravariant functor H into the category MV(C)G of MV-algebras generated by perfect MV-chains via the operators of direct products, subalgebras and direct limits. Conversely, the category MV(C)G is transferred into the category GS by means of a contravariant functor P. Moreover, it is shown that the functor H is faithful, the functor P is full and the both functors are dense. The description of finite coproduct of algebras, which are isomorphic to Chang algebra, is given. Using duality a characterization of projective algebras in MV(C)G is given.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11386/4668345
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