Free Lukasiewicz implication algebras

نویسنده

J. Patricio Díaz Varela

چکیده

Lukasiewicz implication algebras are the {→, 1}-subreducts of MV algebras. They are the algebraic counterpart of SuperLukasiewicz Implicational Logics. We give a description of free Lukasiewicz implication algebras in the context of McNaughton functions. More precisely, we show that the |X|-free Lukasiewicz implication algebra is isomorphic to ⋃ x∈X [xθ) for a certain congruence θ over the |X|-free MV -algebra. As corollary we describe the free algebras in all subvarieties of Lukasiewicz implication algebras.

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