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- Title
A note on the first-order logic of complete BL-chains.
- Authors
Hajek, Petr; Montagna, Franco
- 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 <BI>B</BI> satisfies all standard BL-tautologies iff for any transfinite sequence (ai: i ∈ I) of elements of <BI>B</BI>, the condition ∧i ∈ I (a2i) = (∧i ∈ Iai)2 holds in <BI>B</BI>. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)
- Subjects
MATHEMATICAL analysis; ALGEBRAIC logic; MATHEMATICAL logic; RELATION algebras; MATHEMATICS
- Publication
Mathematical Logic Quarterly, 2008, Vol 54, Issue 4, p435
- ISSN
0942-5616
- Publication type
Article
- DOI
10.1002/malq.200710058