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 (a(i) : i is an element of I) of elements of B, the condition Lambda(i is an element of I) (a(i)(2)) = (Lambda(i is an element of I) a(i))(2) holds in B.
Hàjek, P., Montagna, F. (2008). A note on the first order logic of complete BL chains. MATHEMATICAL LOGIC QUARTERLY, 54(4), 435-446 [10.1002/malq.200710058].
A note on the first order logic of complete BL chains
MONTAGNA, FRANCO
2008-01-01
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 (a(i) : i is an element of I) of elements of B, the condition Lambda(i is an element of I) (a(i)(2)) = (Lambda(i is an element of I) a(i))(2) holds in B.
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https://hdl.handle.net/11365/7092
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