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A proof of standard completeness for Esteva and Godo’s logic MTL. (English) Zbl 0997.03027
Summary: We show that any at most countable linearly-ordered commutative residuated lattice can be embedded into a commutative residuated lattice on the real unit interval \([0,1]\). We use this result to show that F. Esteva and L. Godo’s logic MTL [Fuzzy Sets Syst. 124, 271-288 (2001; Zbl 0994.03017)] is complete with respect to interpretations into commutative residuated lattices on \([0,1]\). This solves an open problem raised by Esteva and Godo [loc. cit.].

MSC:
03B50 Many-valued logic
03B52 Fuzzy logic; logic of vagueness
03G10 Logical aspects of lattices and related structures
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