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Ralph Mckenzie [23]Ralph N. Mckenzie [1]
  1. On spectra, and the negative solution of the decision problem for identities having a finite nontrivial model.Ralph Mckenzie - 1975 - Journal of Symbolic Logic 40 (2):186-196.
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  2. Finite basis problems and results for quasivarieties.Miklós Maróti & Ralph McKenzie - 2004 - Studia Logica 78 (1-2):293 - 320.
    Let be a finite collection of finite algebras of finite signature such that SP( ) has meet semi-distributive congruence lattices. We prove that there exists a finite collection 1 of finite algebras of the same signature, , such that SP( 1) is finitely axiomatizable.We show also that if , then SP( 1) is finitely axiomatizable. We offer new proofs of two important finite basis theorems of D. Pigozzi and R. Willard. Our actual results are somewhat more general than this abstract (...)
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  3.  14
    Finite basis problems and results for quasivarieties.Miklós Maróti & Ralph Mckenzie - 2004 - Studia Logica 78 (1-2):293-320.
    Let \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$\mathcal{K}$$ \end{document} be a finite collection of finite algebras of finite signature such that SP(\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$\mathcal{K}$$ \end{document}) has meet semi-distributive congruence lattices. We prove that there exists a finite collection \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$\mathcal{K}$$ \end{document}1 of finite algebras of the same signature, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$\mathcal{K}_1 \supseteq (...)
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  4.  8
    Definability in lattices of equational theoris.Ralph McKenzie - 1971 - Annals of Mathematical Logic 3 (2):197-237.
  5.  82
    On some small cardinals for Boolean algebras.Ralph Mckenzie & J. Donald Monk - 2004 - Journal of Symbolic Logic 69 (3):674-682.
    Assume that all algebras are atomless. (1) $Spind(A x B) = Spind(A) \cup Spind(B)$ . (2) $(\prod_{i\inI}^{w} = {\omega} \cup \bigcup_{i\inI}$ $Spind(A_{i})$ . Now suppose that $\kappa$ and $\lambda$ are infinite cardinals, with $kappa$ uncountable and regular and with $\kappa \textless \lambda$ . (3) There is an atomless Boolean algebra A such that $\mathfrak{u}(A) = \kappa$ and $i(A) = \lambda$ . (4) If $\lambda$ is also regular, then there is an atomless Boolean algebra A such that $t(A) = \mathfrak{s}(A) = (...)
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  6. Decidable discriminator varieties from unary varieties.Stanley Burris, Ralph Mckenzie & Matthew Valeriote - 1991 - Journal of Symbolic Logic 56 (4):1355-1368.
    We determine precisely those locally finite varieties of unary algebras of finite type which, when augmented by a ternary discriminator, generate a variety with a decidable theory.
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  7.  92
    The Jónsson-Kiefer Property.Kira Adaricheva, Miklos Maróti, Ralph Mckenzie, J. B. Nation & Eric R. Zenk - 2006 - Studia Logica 83 (1-3):111-131.
    The least element 0 of a finite meet semi-distributive lattice is a meet of meet-prime elements. We investigate conditions under which the least element of an algebraic, meet semi-distributive lattice is a (complete) meet of meet-prime elements. For example, this is true if the lattice has only countably many compact elements, or if |L| < 2ℵ0, or if L is in the variety generated by a finite meet semi-distributive lattice. We give an example of an algebraic, meet semi-distributive lattice that (...)
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  8.  46
    The Jónsson-Kiefer Property.Kira Adaricheva, Ralph Mckenzie, Eric Richard Zenk, M. Mar & James B. Nation - 2006 - Studia Logica 83 (1-3):111-131.
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  9. University of Illinois at Chicago, Chicago, IL, June 1–4, 2003.Gregory Cherlin, Alan Dow, Yuri Gurevich, Leo Harrington, Ulrich Kohlenbach, Phokion Kolaitis, Leonid Levin, Michael Makkai, Ralph McKenzie & Don Pigozzi - 2004 - Bulletin of Symbolic Logic 10 (1).
     
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  10.  5
    Algebras, Lattices, and Varieties.Ralph McKenzie, McNulty N., F. George & Walter F. Taylor - 1987 - Wadsworth & Brooks.
    This book presents the foundations of a general theory of algebras. Often called “universal algebra”, this theory provides a common framework for all algebraic systems, including groups, rings, modules, fields, and lattices. Each chapter is replete with useful illustrations and exercises that solidify the reader's understanding. The book begins by developing the main concepts and working tools of algebras and lattices, and continues with examples of classical algebraic systems like groups, semigroups, monoids, and categories. The essence of the book lies (...)
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  11.  24
    Bradd Hart and Matthew Valeriote. A structure theorem for strongly abelian varieties with few models. The journal of symbolic logic, vol. 56 , pp. 832–852. - Bradd Hart and Sergei Starchenko. Addendum to “A structure theorem for strongly abelian varieties.”The journal of symbolic logic., vol. 58 , pp. 1419–1425. - Bradd Hart, Sergei Starchenko, and Matthew Valeriote. Vaught's conjecture for varieties. Transactions of the American Mathematical Society, vol. 342 , pp. 173–196. - B. Hart and S. Starchenko. Superstable quasi-varieties. Annals of pure and applied logic, vol. 69 , pp. 53–71. - B. Hart, A. Pillay, and S. Starchenko. Triviality, NDOP and stable varieties. Annals of pure and applied logic., vol. 62 , pp. 119–146.Ralph McKenzie - 1999 - Journal of Symbolic Logic 64 (4):1820-1821.
  12.  36
    Negative solution of the decision problem for sentences true in every subalgebra of < n, + >.Ralph Mckenzie - 1971 - Journal of Symbolic Logic 36 (4):607-609.
  13.  13
    [Omnibus Review].Ralph McKenzie - 1999 - Journal of Symbolic Logic 64 (4):1820-1821.
    Bradd Hart, Matthew Valeriote, A Structure Theorem for Strongly Abelian Varieties with Few Models.Bradd Hart, Sergei Starchenko, Addendum to "A Structure Theorem for Strongly Abelian Varieties.".Bradd Hart, Sergei Starchenko, Matthew Valeriote, Vaught's Conjecture for Varieties.B. Hart, S. Starchenko, Superstable Quasi-Varieties.B. Hart, A. Pillay, S. Starchenko, Triviality, NDOP and Stable Varieties.
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  14.  43
    Recursive inseparability for residual Bounds of finite algebras.Ralph McKenzie - 2000 - Journal of Symbolic Logic 65 (4):1863-1880.
    We exhibit a construction which produces for every Turing machine T with two halting states μ 0 and μ -1 , an algebra B(T) (finite and of finite type) with the property that the variety generated by B(T) is residually large if T halts in state μ -1 , while if T halts in state μ 0 then this variety is residually bounded by a finite cardinal.
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  15.  13
    Kirby A. Baker. Equational axioms for classes of lattices. Bulletin of the American Mathematical Society, vol. 77 , pp. 97–102. [REVIEW]Ralph McKenzie - 1974 - Journal of Symbolic Logic 39 (1):184.
  16.  7
    Review: Kirby A. Baker, Equational Axioms for Classes of Lattices. [REVIEW]Ralph McKenzie - 1974 - Journal of Symbolic Logic 39 (1):184-184.