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  1. Universal Equational Theories and Varieties of Algebras.Don Pigozzi - 1979 - Annals of Pure and Applied Logic 17 (1):117.
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  • Externally Compatible Abelian Groups of the Type (2,1,0).Krystyna Mruczek-Nasieniewska - 2006 - Logic and Logical Philosophy 15 (3):239-250.
    In [4] the lattice of all subvarieties of the variety G n Ex defined by so called externally compatible identities of Abelian groups together with the identity x n ≈ y n , for any n ∈ N and n ≥ 1 was described. In that paper classes of models of the type (2,1) where considered. It appears that diagrams of lattices of subvariaties defined by externally compatible identities satisfied in a given equational theory depend on the language of the (...)
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  • Regular Equations and Unification Theory.Ewa Graczynska - 1989 - Bulletin of the Section of Logic 18 (1):33-39.
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  • The Absence of Multiple Universes of Discourse in the 1936 Tarski Consequence-Definition Paper.John Corcoran & José Miguel Sagüillo - 2011 - History and Philosophy of Logic 32 (4):359 - 374.
    This paper discusses the history of the confusion and controversies over whether the definition of consequence presented in the 11-page 1936 Tarski consequence-definition paper is based on a monistic fixed-universe framework?like Begriffsschrift and Principia Mathematica. Monistic fixed-universe frameworks, common in pre-WWII logic, keep the range of the individual variables fixed as the class of all individuals. The contrary alternative is that the definition is predicated on a pluralistic multiple-universe framework?like the 1931 Gödel incompleteness paper. A pluralistic multiple-universe framework recognizes multiple (...)
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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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  • Finitely-Based Subvarieties of Hilbert Algebras Are 2-Based.Leonardo Cabrer - 2011 - Bulletin of the Section of Logic 40 (3/4):215-220.
  • Definability in Lattices of Equational Theoris.Ralph McKenzie - 1971 - Annals of Mathematical Logic 3 (2):197-237.
  • Universal Horn Classes Categorical or Free in Power.Steven Givant - 1978 - Annals of Mathematical Logic 15 (1):1-53.
  • The Lattice of Subvarieties of the Variety Defined by Externally Compatible Identities of Abelian Groups of Exponent N.Katarzyna Gajewska-Kurdziel & Krystyna Mruczek-Nasieniewska - 2007 - Studia Logica 85 (3):361-379.
    The lattices of varieties were studied in many works (see [4], [5], [11], [24], [31]). In this paper we describe the lattice of all subvarieties of the variety $G_{Ex}^n$ defined by so called externally compatible identities of Abelian groups and the identity xⁿ ≈ yxⁿ. The notation in this paper is the same as in [2].
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  • The Varieties Defined by P - Compatible Identities of Modular Ortholattices.Krystyna Mruczek-Nasieniewska - 2010 - Studia Logica 95 (1-2):21 - 35.
    In the present paper we give syntactical and semantical characterization of the class of algebras defined by P-compatible identities of modular ortholattices. We also describe the lattice of some subvarieties of the variety MOL Ex defined by so called externally compatible identities of modular ortholattices.
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  • The Varieties Defined by P-Compatible Identities of Modular Ortholattices.Krystyna Mruczek-Nasieniewska - 2010 - Studia Logica 95 (1-2):21-35.
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