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  1. Interpolation and Beth’s property in propositional many-valued logics: A semantic investigation.Franco Montagna - 2006 - Annals of Pure and Applied Logic 141 (1):148-179.
    In this paper we give a rather detailed algebraic investigation of interpolation and Beth’s property in propositional many-valued logics extending Hájek’s Basic Logic [P. Hájek, Metamathematics of Fuzzy Logic, Kluwer, 1998], and we connect such properties with amalgamation and strong amalgamation in the corresponding varieties of algebras. It turns out that, while the most interesting extensions of in the language of have deductive interpolation, very few of them have Beth’s property or Craig interpolation. Thus in the last part of the (...)
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  • ŁΠ logic with fixed points.Luca Spada - 2008 - Archive for Mathematical Logic 47 (7-8):741-763.
    We study a system, μŁΠ, obtained by an expansion of ŁΠ logic with fixed points connectives. The first main result of the paper is that μŁΠ is standard complete, i.e., complete with regard to the unit interval of real numbers endowed with a suitable structure. We also prove that the class of algebras which forms algebraic semantics for this logic is generated, as a variety, by its linearly ordered members and that they are precisely the interval algebras of real closed (...)
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  • Minimum bases for equational theories of groups and rings: the work of Alfred Tarski and Thomas Green.George F. McNulty - 2004 - Annals of Pure and Applied Logic 127 (1-3):131-153.
    Suppose that T is an equational theory of groups or of rings. If T is finitely axiomatizable, then there is a least number μ so that T can be axiomatized by μ equations. This μ can depend on the operation symbols that occur in T. In the 1960s, Tarski and Green completely determined the values of μ for arbitrary equational theories of groups and of rings. While Tarski and Green announced the results of their collaboration in 1970, the only fuller (...)
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  • Horn Sentences of Small Size in Identity Theory.G. Marongiu & S. Tulipani - 1986 - Mathematical Logic Quarterly 32 (25-30):439-444.
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  • Notions of density that imply representability in algebraic logic.Hajnal Andréka, Steven Givant, Szabolcs Mikulás, István Németi & András Simon - 1998 - Annals of Pure and Applied Logic 91 (2-3):93-190.
    Henkin and Tarski proved that an atomic cylindric algebra in which every atom is a rectangle must be representable . This theorem and its analogues for quasi-polyadic algebras with and without equality are formulated in Henkin, Monk and Tarski [13]. We introduce a natural and more general notion of rectangular density that can be applied to arbitrary cylindric and quasi-polyadic algebras, not just atomic ones. We then show that every rectangularly dense cylindric algebra is representable, and we extend this result (...)
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