David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
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Studia Logica 50 (3-4):375 - 384 (1991)
The infinite-valued logic of ukasiewicz was originally defined by means of an infinite-valued matrix. ukasiewicz took special forms of negation and implication as basic connectives and proposed an axiom system that he conjectured would be sufficient to derive the valid formulas of the logic; this was eventually verified by M. Wajsberg. The algebraic counterparts of this logic have become know as Wajsberg algebras. In this paper we show that a Wajsberg algebra is complete and atomic (as a lattice) if and only if it is a direct product of finite Wajsberg chains. The classical characterization of complete and atomic Boolean algebras as fields of sets is a particular case of this result.
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References found in this work BETA
Alfred Tarski (1956). Logic, Semantics, Metamathematics. Oxford, Clarendon Press.
Antoni Torrens (1987). W-Algebras Which Are Boolean Products of Members of SR and CW-Algebras. Studia Logica 46 (3):265 - 274.
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