A note on the first‐order logic of complete BL‐chains
Petr Hájek, Franco Montagna · Mathematical logic quarterly · 2008
Abstract In [10] it is claimed that the set of predicate tautologies of all complete BL‐chains and the set of all standard tautologies (i. e., the set of predicate formulas valid in all standard BL‐algebras) coincide. As noticed in [11], this claim is wrong. In this paper we show that a complete BL‐chain B satisfies all standard BL‐tautologies iff for any transfinite sequence (ai: i ∈ I) of elements of B, the condition ∧i ∈ I (a2i ) = (∧i ∈ I ai)2 holds in B. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)