BOOKS

  1. [with R. McKenzie]
    Decidability and Boolean Representations. Memoirs A.M.S. No. 246, July 1981.
    [MR 83j : 03024]

  2. [with H.P. Sankappanavar]
    A Course in Universal Algebra. Graduate Texts in Mathematics No. 78, Springer-Verlag, 1981.
    [MR 83k : 08001]

  3. Logic for Mathematics and Computer Science. Prentice-Hall, 1998. ISBN 0-13-285974-2

  4. Number Theoretic Density and Logical Limit Laws. Amer. Math. Soc. 2001 ISBN 0-8218-26666-2
    [MR 2002c:03060 ]

PAPERS

  1. Representation theorems for closure spaces.
    Colloq. Math. 19 (1968), 187 - 193.
    [MR 37 #2659] PDF (18.5 Megs)

  2. Closure homomorphisms.
    J. of Algebra 15 (1970), 68 - 71.
    [MR 40 #7174] PDF (15.5 Megs)

  3. A note on varieties of unary algebras.
    Colloq. Math. 22 (1971), 195 - 196.
    [MR 43 #6147] PDF (6 Megs)

  4. [with E. Nelson]
    Embedding the dual of Πm in the lattice of equational classes of commutative semigroups.
    Proc. AMS 30 (1971), 37 - 39.
    [MR 44 #2857] PDF (7.0 Megs)

  5. [with E. Nelson]
    Embedding the dual of Π∞ in the lattice of equational classes of semigroups.
    Algebra Universalis 1 (1971), 248 - 253.
    [MR 45 #5257] PDF (19.5 Megs)

  6. On the structure of the lattice of equational classes L(τ).
    Algebra Universalis 1 (1971), 39 - 45.
    [MR 45 #144] PDF (10.5 Megs)

  7. The structure of closure congruences.
    Colloq. Math. 24 (1971), 3 - 5.
    [MR 46 #3403] PDF (8.5 Megs)

  8. Embedding algebraic closures in 2-ary closure spaces.
    Portugal Math. 31 (1972), 183 - 185.
    [MR 46 #5206]

  9. Models in equational theories of unary algebras.
    Algebra Universalis 1 (1972), 386 - 392.
    [MR 45 #3287]

  10. Scott sentences and a problem of Vaught for mono-unary algebras.
    Fund. Math. 80 (1974), 111 - 115.
    [MR 48 #5817] PDF (13.0 Megs)
    (NOTE: this paper has a serious gap in the proof.)

  11. Weights of denumerable topological spaces.
    Fund. Math. 85 (1974), 25 - 27.
    [MR 50 #8408] PDF (7.1 Megs)

  12. Boolean powers.
    Algebra Universalis 5 (1975), 341 - 360.
    [MR 56 #5393] PDF (33 Megs)

  13. [with HP Sankappanavar]
    Lattice-theoretic decision problems in universal algebra.
    Algebra Universalis 5 (1975), 163 - 177.
    [MR 52 #13359] PDF (23 Megs)

  14. Separating sets in modular lattices with applications to congruence lattices.
    Algebra Universalis 5 (1975), 213 - 223.
    [MR 52 #10524]

  15. Subdirect representations in axiomatic classes.
    Colloq. Math. 34 (1976), 191 - 196. PDF (13.0 Megs)

  16. An example concerning definable principal congruences.
    Algebra Universalis 7 (1977), 403 - 404.
    [MR 56 #216] PDF (2.0 Megs)

  17. Bounded Boolean powers and ≡ n.
    Algebra Universalis 8 (1978), 137 - 138.
    [MR 56 #8467]. PDF (2 Megs)

  18. [with E. Jeffers]
    On the simplicity and subdirect irreducibility of Boolean ultrapowers.
    Colloq. Math. 39 (1978), 215 - 218.
    [MR 80d: 0306] PDF (5.5 Megs)

  19. Remarks on reducts of varieties.
    Proceedings of the 1978 conference on Universal Algebra in Esztergom, 161 - 168. PDF (2 Megs)

  20. Rigid Boolean Powers.
    Algebra Universalis 8 (1978), 264 - 265.
    [MR 57 #3042]. PDF (2.5 Megs)

  21. [with J. Lawrence]
    Definable principal congruences in varieties of groups and rings.
    Algebra Universalis 9 (1979), 152 - 164
    [MR 80c: 08004] PDF (14.5 Megs)
    A correction to ...
    Algebra Universalis 13 (1981), 264 - 267. PDF (3.5 Megs)

  22. On Baker's finite basis theorem for congruence distributive varieties.
    Proc. AMS 73 (1979), 141 - 148.
    [MR 80b: 08003] PDF (14.5 Megs)

  23. [with H. Werner]
    Sheaf constructions and their elementary properties.
    Trans AMS 248 (1979), 269 - 309.
    [MR 82d: 03049]

  24. Free algebras as subdirect products.
    Algebra Universalis 11 (1980), 133 - 134. PDF (220 K)

  25. [with H. Werner]
    Remarks on Boolean products.
    Algebra Universalis 10 (1980), 333 - 334.
    [MR 81f: 08001] PDF (14 Megs)

  26. [with R. McKenzie]
    Decidable varieties with modular congruence lattices.
    Bull. AMS 4 (1981), 350 - 352 (Research announcement). PDF (0.5 Meg)

  27. [with J. Lawrence]
    Two examples concerning the definability of the disjointness property of principal congruences.
    Algebra Universalis 12 (1981), 148 - 153. PDF (6.5 Megs)

  28. A note on directly indecomposable algebras.
    Algebra Universalis 14 (1982), 132 - 133. PDF (0.23 Megs)

  29. The first-order theory of Boolean algebras with a distinguished group of automorphisms.
    Algebra Universalis 15 (1982), 151 - 161.
    [MR 84f : 03008] PDF (1 Meg)

  30. [with J. Lawrence]
    Two undecidability results using modified Boolean powers.
    Can J. Math. 34 (1982), 500 - 505.
    [MR 83k : 03051] PDF (10.7 Megs)

  31. Boolean constructions.
    Universal Algebra and Lattice Theory, Proceedings, Puebla 1982,
    Springer Lecture Notes #1004 (1983), 67 - 90.
    [MR 85d : 08010] PDF (9 Megs)

  32. [with M. Valeriote]
    Expanding varieties by monoids of endomorphisms.
    Algebra Universalis 17 (1983), 150 - 169.
    [MR 86b : 08004] PDF (2.5 Megs)

  33. Model companions for finitely generated universal Horn classes.
    J Symbolic Logic 49 (1984), 68 - 74.
    [MR 85g : 03052] PDF (10.6 Megs)

  34. A simple proof of the hereditary undecidability of the theory of lattice-ordered abelian groups.
    Algebra Universalis 20 (1985), 400 - 401.
    [MR 87g : 06043] PDF (0.3 Megs)

  35. Discriminator polynomials and arithmetical varieties.
    Algebra Universalis 20 (1985), 397 - 399.
    [MR 87c : 08009] PDF (0.5 Megs)

  36. Iterated discriminator varieties have undecidable theories.
    Algebra Universalis 21 (1985), 54 - 61.
    [MR 87g : 08018] PDF (7.0 Megs)

  37. [with D. Clark]
    Elementary and algebraic properties of the Arens-Kaplansky constructions.
    Algebra Universalis 22 (1986), 50 - 93.
    [MR 88a : 08016]

  38. [with M.H. Albert]
    Finite axiomatizations for existentially closed posets and semilattices.
    Order 3 (1986), 169 - 178.

  39. Remarks on the Fraser Horn Property.
    Algebra Universalis 32 (1986), 19 - 21.
    [MR 88b : 08009] PDF (4 Megs)

  40. A note on algebraically and existentially closed structures.
    Algebra Universalis 24 (1987), 186 - 187.
    [MR 88k : 03075] PDF (2 Megs)

  41. [with R. Willard]
    Finitely many primitive positive clones.
    Proc. Amer. Math. Soc. 101 (1987), 427 - 430.
    [MR 89a : 08002a]

  42. Primitive positive clones which are endomorphism clones.
    Algebra Universalis 40 (1987), 41 - 49.
    [MR 89a : 08002b]

  43. The model completion of L-structures.
    Zeitschr. f. math. Logik u. Grundlagen Math. 33 (1987), 313 - 314. PDF (3 Megs)

  44. [with M. Albert]
    Bounded obstructions, model companions and amalgamation bases.
    Zeitschr. f. math. Logik u. Grundlagen Math. 34 (1988), 109 - 115.
    Correction to EC Semilattice Axioms PDF (225 K)

  45. Decidable model companions.
    Zeitschr. f. math. Logik u. Grundlagen Math. 35 (1989), 225 - 227.

  46. [with D. Bigelow ]
    Boolean algebras of factor congruences.
    Acta Math Szeged 54 (1990), 11 - 20.

  47. [with J. Lawrence]
    Unification in commutative rings is not finitary.
    Information Processing Letters 36 (1990), 37 - 38.

  48. [with R. McKenzie, M. Valeriote]
    Decidable discriminator varieties from unary varieties.
    J. Symbolic Logic 56 (1991), 1355 - 1368.

  49. [with J. Lawrence]
    Term rewrite systems for finite fields.
    Internat. J of Algebra and Computation 1 (1991), 353 - 369.
    Preprint DVI PS PDF

  50. Discriminator varieties and symbolic computation.
    J. Symbolic Computation 13 (1992), 175 - 207.

  51. [with S. Lee]
    Small models of the High School Identities.
    Internat. J. of Algebra and Computation 2 (1992), 139 - 178.
    Preprint PDF

  52. [w. J. Lawrence]
    The equivalence problem for finite rings.
    J. Symbolic Computation 15 (1993), 67 - 71.

  53. [with S. Lee]
    Tarski's High School Identities.
    Amer. Math. Monthly 100 (1993), 231 - 236.

  54. [w. Isabel Ferrierem]
    Decidable varieties of hoops.
    Reports on Math. Logic, 28 (1994), 53 - 59.

  55. Model companions with finitely many countable models.
    Mathematical Logic Quarterly 40 (1994), 141 - 142.

  56. Computers and universal algebra: some directions.
    Algebra Universalis 34 (1995), 61 - 71.
    Preprint PS PDF

  57. Polynomial time uniform word problems.
    Math. Logic Quarterly 41 (1995), 173 - 182.
    Preprint DVI PS PDF

  58. [w. Joel Berman]
    A computer study of 3-element groupoids.
    In Logic and Algebra, (The Proceedings of the Magari Conference),
    edited by A. Ursini and P. Agliano (1996), 379 - 430, Marcel Dekker, Inc.
    Part 1 PDF (the discussion)
    Part 2 PDF (the groupoid tables)

  59. [w. Pawel Idziak]
    A directly representable variety has a discrete first-order law.
    International J. of Algebra and Computation, 6 (1996), 269 - 276.

  60. [w. Ross Willard]
    Problem 17 of Grätzer and Kisielewicz.
    Algebra Universalis, 36 (1996), 573 - 575.

  61. [w. A. Sárközy]
    Fine spectra and limit laws I: First-order laws.
    Can. J. Math. 49 (1997), 468 - 498.
    [MR 98k : 03076a]

  62. [w. K. Compton, A. Odlyzko, B. Richmond]
    Fine spectra and limit laws II: First-order 0-1 laws.
    Can. J. Math. 49 (1997), 641--652.

  63. Spectrally determined first-order limit laws.
    Logic and Random Structures, ed. by Ravi Boppana and James Lynch.
    DIMACS Ser. Discrete Math. Theoret. Comput.
    Sci. 33 , 33--52. Amer. Math. Soc., Providence, RI, 1997.
    [MR 98k : 03076b]

  64. Abstract number systems and logical limit laws. Dedicated to the memory of John Knopfmacher.
    Quaest. Math. 24 (2001), no. 3, 349--354.
    [MR 2003e:11106]

  65. Boolean Products of Indecomposables
    Algebra Universalis 48 (2002), no. 4, 497--499
    Preprint [ PS ] [ DVI ] [ PDF ]

  66. [with Jason Bell]
    Asymptotics for Logical Limit Laws.
    When the Growth of the Components is in an RT Class.
    Trans. Amer. Math. Soc. 355, no. 9 , (2003), 3777--3794.
    [MR 2004h:03072 ] Preprint [ PS ] [ DVI ] [ PDF ]

  67. [with Jason Bell]
    Partition Identities I. Sandwich Theorems and 0-1 Laws
    Electron. J. Combin. 11 (2004), no. 1, Research Paper 49, 25 pp. (electronic).
    [MR 2005i:11144] Preprint [ PS ] [ DVI ] [ PDF ]

  68. [with John Lawrence]
    Results on the Equivalence Problem for Finite Groups
    Algebra Universalis 52 (2004), no. 4, 495--500.
    [MR 2006d:08005 ] Preprint [ PS ] [ DVI ] [ PDF ]

  69. The Equational Theory of a Nontrivial Discriminator Variety is Co-NP Hard
    Algebra Universalis 52 (2004), no. 4, 487--494.
    [MR 2006a:08007 ] Preprint [ PS ] [ DVI ] [ PDF ]

  70. [with Karen Yeats]
    The Saga of the High School Identities.
    Algebra Universalis 52 (2004), no. 2-3, 325--342
    [MR 2006f:03049] Preprint [ PS ] [ DVI ] [ PDF ]

  71. [with Jason Bell and Karen Yeats ]
    Counting Rooted Trees: The Universal Law t(n) ~ C ⋅ ρ −n ⋅ n −3/2
    The Electron. J. Combin. 13 (2006), #R63 [64pp.]
    [MR 2007c:05012 ]

  72. [with Jason Bell]
    Partition Identities II. The Results of Bateman and Erdos
    J. Number Theory 117 (2006), No. 1, 160--190.
    [MR 2006k:11199] Preprint [ PS ] [ DVI ] [ PDF ]

  73. [ with Karen Yeats ]
    Sufficient conditions for a labelled 0--1 law.
    Discrete Math. Theor. Comput. Sci. 10 (2008), no.1, 147-156.
    [MR 2009b:03087 ] Preprint [ PS ] [ PDF ]

  74. The Algebra of Logic Tradition.
    The Stanford Encyclopedia of Philosophy, (2009).

  75. George Boole.
    The Stanford Encyclopedia of Philosophy, (2010).

  76. [with Jason Bell and Karen Yeats ]
    Characteristic points of recursive systems.
    The Electron. J. Combin. 17 (2010), #R121 [34pp.]

  77. [with Jason Bell and Karen Yeats ]
    Spectra and systems of equations.
    pp. 43--96, in ``Model Theoretic Methods in Combinatorics'',
    in the series Contemporary Mathematics of the AMS, Vol 558 (2011),
    edited by M. Grohe and J.A. Makowsky.

  78. [with Jason Bell]
    Compton's method for proving logical limit laws.
    pp. 97--128, in ``Model Theoretic Methods in Combinatorics'',
    in the series Contemporary Mathematics of the AMS, Vol 558 (2011),
    edited by M. Grohe and J.A. Makowsky.

  79. [with Jason Bell and Karen Yeats]
    Monadic second-order classes of forests with a monadic second-order 0-1 law.
    Discrete Math. Theor. Comput. Sci. 14 (2012), no. 1, 87--108.
    Preprint available at http://arxiv.org/abs/1004.1128

  80. [with Jason Bell and Karen Yeats ]
    On the set of zero coefficients of a function satsifying a linear differential equation.
    Math. Proc. of the Cambr. Phil. Soc., 153 (2012), No. 02, 235--247.
    Preprint available at http://arxiv.org/abs/1105.6078 [11pp.]

  81. [with H.P. Sankappanavar]
    The Horn theory of Boole's partial algebras.
    Bull. Assoc. Symb. Logic, 19, No.1 (March 2013), pp. 97--105.

    PREPRINTS

  82. [with H.P. Sankappanavar]
    Boole's Method I. A Modern Version
    [ PDF ]

  83. [with Jason Bell]
    Admissible Dirichlet series
    [ PS ] [ DVI ] [ PDF ]

  84. [with Jason Bell]
    Dirichlet Density Extends Global Asymptotic Density in Multiplicative Systems
    [ PS ] [ DVI ] [ PDF ]

    LECTURE NOTES (unpublished)

  85. Existentially Closed Structures and Boolean Products. (Seminar Notes)
    [ PS ] [ PDF ]
  86. Foundations of Formal Theorem Proving.

    HISTORY OF LOGIC

  87. Contributions of the Logicians

  88. My Book Review of A Boole Anthology
    [ PS ] [ DVI ] [ PDF ]

  89. The Laws of Boole's Thought.
    [ PS ] [ DVI ] [ PDF ]

  90. A Fragment of Boole's Algebraic Logic Suitable for Traditional Syllogistic Logic.
    [ PS ] [ DVI ] [ PDF ]

Reviews for Journals

  1. Reviews of five papers on undecidable properties of finite sets of equations. J Symbolic Logic 47 (1982), 903 - 904.

  2. Review of ``Commutator Theory for Congruence Modular Varieties'' by R. Freese and R. McKenzie. Bull. Amer. Math. Soc. 20 (1989), 94 - 96.