# Ralph McKenzie

Distinguished Professor

#### Research Interests

Algebra and Logic.

#### Publications

118. (with K. Kearnes and P. Markovic) *A note on Maltsev conditions for omitting type locally finite varieties, *(in progress).

117. (with E. Aichinger, P. Mayr) *On the number of algebraic structures,* Journal of the European Mathematical Society (to appear).

116. (with P. Markovic, M. Maroti) * Finitely related clones and algebras with cube-terms,* Order, **29(2)** (2012), 345-359.

115. (with P. Markovic) * Few subpowers, congruence distributivity, and near-unanimity terms,* Algebra Universalis **58** (2008), 119-128. [PDF]

114. (with J. Jezek) * Definability in substructure orderings, IV: finite lattices,* Algebra Universalis **61** (2009), 301-312. [PDF]

113. (with J. Jezek) * Definability in substructure orderings, III: finite distributive lattices,* Algebra Universalis **61** (2009), 283-300. [PDF]

112. (with J. Jezek) * Definability in substructure orderings, II: finite ordered sets,* Order **27** (2010), 115-145. [PDF]

111. (with J. Jezek) * Definability in substructure orderings, I: finite semilattices,* Algebra Universalis **61** (2009), 59-75. [PDF]

110. (with L. Barto, M. Kozik, M. Maróti and T. Niven) * Congruence modularity implies cyclic terms for finite algebras, *Algebra Universalis **61(3)** (2009), 365-380. [PDF]

109. (with W. Dziobiak and J. Jezek) * Avoidable structures, II: finite distributive lattices and nicely structured ordered sets,* Algebra Universalis **60** (2009), 259-291. [PDF]

108. (with W. Dziobiak and J. Je�ek) * Avoidable structures, I: ordered sets, semilattices and lattices,* Algebra Universalis **60 **(2009), 247-258. [PDF]

107. (with P. Idziak, P. Markovíc, M. Valeriote, R. Willard) * Tractability and learnability arising from algebras with few subpowers,* SIAM J. Comp. (to appear)

106. (with P. Idziak, P. Markovíc, M. Valeriote, R. Willard) * Tractability and learnability arising from algebras with few subpowers,* Proceedings of the 22^{nd} Annual IEEE Symposium on Logic in Computer Science, 221-230. [PDF]

105. (with J. Berman, P. Idziak, P. Markovíc, M. Valeriote, R. Willard) * Varieties with few subalgebras of powers,* Transactions AMS **362** (2009), 1145-1173. [PDF]

104. (with W. Dziobiak, M. Maroti, A. Nurakuno and R. Willard) * The weak extension property and finite axiomatizability for quasivarieties,* Fundamenta Mathematicae **202** (2009), 199-223. [PDF]

* *103. (with P.M. Idziak and M. Valeriote)* The structure of locally finite varieties with polynomially many models,* Journal of the American Mathematical Society

**22, no. 1**(2009), 119--165. [PDF

102. (with B. Davey, M. Jackson and M. Maroti) * Principal and syntactic congruences in congruence-distributive and congruence-permutable varieties,* J. Austral. Math. Soc. **85** (2008), 59-74.

101. (with M. Maroti) * Existence theorems for weakly symmetric operations,* Algebra Universalis **59, 3-4** (2008), 463-489. [PDF]

100. (with P. Dapic, J. Je�ek, P. Markovic and D. Stanovský) * Star-linear equational theories of groupoids,* Algebra Universalis ** 56 (3/4)** 357--397. (2007),

99. (with D. Stanovský) * Every quasigroup is isomorphic to a subdirectly irreducible quasigroup modulo its monolith,* Acta Math. Sci. Szeged ** 72** (2006), 59--64.

98. (with K. Adaricheva, M. Maróti, J.B. Nation and E.R. Zenk) * The Jónsson-Kiefer property,* Studia Logica **83** (2006), 111--131.[PDF]

97. (with M. Jackson) * Interpreting graph colourability in finite semigroups,* International Journal of Algebra and Computation ** 16**, No. 1 (2006), 119--140. [PDF]

96. (with John Snow) Congruence modular varieties: commutator theory and its uses, in: Structural Theory of Automata, Semigroups and Universal Algebra, Edited by V.B.Kudryavtsev and I. G. Rosenberg, NATO Science Series II: Mathematics, Physics and Chemistry -- Vol. 207, pp. 273--329, 2005, Springer.

95. (with J. Jezek and M. Maroti) * Quasi-equational theories of flat algebras,* Czech. Math. J. ** 55**, No. 3 (2005), 665--675.

94. (with J. D. Monk) * On some small cardinals for Boolean algebras,* Journal of Symbolic Logic ** 69** (2004), 674--682.

93. (with M. Maroti) * Finite basis problems and results for quasivarieties,* Studia Logica ** 78** (2004), 293--320. [PDF]

92. *The zig-zag property and exponential cancellation of ordered sets,* Order ** 20** (2004), 185--221.[PDF]

91. *Locally finite varieties with large free spectra,* Algebra Universalis ** 47** (2002), 303--318.

90. (with R. Freese, J. Je�ek, P. Jipsen, P. Markovic M. Maroti) * The variety generated by order algebras,* Algebra Universalis ** 47** (2002), 103--138.

89. *Residual smallness relativized to congruence types, I,* Journal of Pure and Applied Algebra ** 163** (2001), 209--220.

88. (with P. M. Idziak) * Varieties with polynomially many models,* Fundamenta Mathematicae ** 170** (2001), 53--68.

87. (with J. Jezek) * The variety generated by equivalence algebras,* Algebra Universalis ** 45**(2001), 211--219.

86. (with J. Wood) * The type-set of a variety is not computable,* International Journal of Algebra and Computation ** 11** (2001), 89--130.

85. (with M. Droste, D. Kuske, R. Pöschel) * Complementary closed relational clones are not always Krasner clones,* Algebra Universalis ** 45** (2001), 155--160.

84. *Recursive inseparability for residual bounds of finite algebras,* Journal of Symbolic Logic ** 65**, no. 4 (2000), 1863--1880.

83. (with J. Jezek, P. Markovic and M. Maroti) * Equations of tournaments are not finitely based,* Discrete Mathematics ** 211** (2000), 243--248.

82. *Arithmetic of finite ordered sets: cancellation of exponents, II,* Order ** 17** (2000), 309--332.

81. *Arithmetic of finite ordered sets: cancellation of exponents, I,* Order ** 16** (1999), 313--333.

80. Review of five papers of B. Hart, A. Pillay, S. Starchenko and M. Valeriote in J. Symbolic Logic [when][about 1999].

79. (with J. Jezek, P. Markovic and M. Maroti) * The variety generated by tournaments,* Acta Univ. Carolinae, Math. et Phy. ** 40** (1999), 21--41.

78. (with K. Kaarli) * Affine complete varieties are congruence distributive,* Algebra Universalis ** 38** (1997), 329--354.

77. (with B.M. Schein) * Every semigroup is isomorphic to a transitive semigroup of binary relations,* Transactions Amer. Math. Soc. ** 349** (1997), 271--285.

76. *An algebraic version of categorical equivalence for varieties and more general algebraic categories,* in: * Logic and Algebra* (Proceedings of the Magari Conference, Siena), A. Ursini and P. Aglianó Eds., Marcel Dekker, New York, 1996.

75. *Tarski's finite basis problem is undecidable,* International Journal of Algebra and Computation ** 6** (1996), 49--104.

74. *The residual bound of a finite algebra is not computable,* International Journal of Algebra and Computation ** 6** (1996), 29--48.

73. *The residual bounds of finite algebras,* International Journal of Algebra and Computation ** 6** (1996), 1--28.

72. (with B. Davey and L. Heindorf) * Near unanimity: an obstruction to general duality theory,* Algebra Universalis ** 33** (1995), 428--439.

71. (with B. Davey, J. B. Nation and P. P. Palfy) * Braids and their monotone clones,* Algebra Universalis ** 32** (1994), 153--176.

70. *On minimal simple lattices,* Algebra Universalis ** 32** (1994), 63--103.

69. (Russian translation of 52). Mir, 1993. Yu. Ershov, V. Gorbunov Eds.

68. (with S. Swierczkowski) * Non-covering in the interpretability lattice of equational theories,* Algebra Universalis ** 30** (1993), 157--170.

67. *On the covering relation in the interpretability lattice of equational theories,* Algebra Universalis ** 30** (1993), 399--421.

66. (with J. Jezek) * Definability in the lattice of equational theories of semigroups, I,* Semigroup Forum ** 46** (1993), 199--245.

65. (with M. Valeriote). * A characterization of decidable locally finite varieties,* in: Proceedings of the International Conference on Algebra honoring A. Malcev. AMS Contemporary Mathematics Volume 131, 1992 (Part 3). pp. 169--185.

64. (with K. Kearnes) * Commutator theory for relatively modular quasivarieties,* Trans. Amer. Math. Soc. **331** (1992), 465--502.

63. (with J. Hyndman and W. Taylor) * k-ary monoids of term operations,* Semigroup Forum ** 44** (1992), 21--52.

62. (with S. Burris and M. Valeriote) * Decidable discriminator varieties from unary varieties,* Jour. Symbolic Logic ** 56** (1991), 1355--1368.

61. *Congruence extension, Hamiltonian and Abelian properties in locally finite varieties,* Algebra Universalis ** 28** (1991), 589--603.

60. *Monotone clones, residual smallness and congruence distributivity,* Bulletin of the Australian Math. Soc. **41** (1990), 283--300.

59. (with C. Bergman) * Minimal varieties and quasivarieties,* Journal of the Australian Math. Soc., Series A **48** (1990), 133--147.

58. (with W. Taylor) * Interpretations of module varieties,* Journal of Algebra ** 135** (1990), 456-493.

57. *Interactions between group theory and the general theory of algebras,* in: ``Groups--Canberra 1989'', Springer Lecture Notes in Mathematics, Volume 1456, 1990. pp. 32--48.

56. *Residually small varieties revisited,* in: Lattices, Semigroups and Universal Algebra (Proceedings of the Lisbon 1988 Conference). Plenum Press, 1990. pp. 185--190.

55. The Structure of Decidable Locally Finite Varieties (with M. Valeriote). Birkhauser, Progress in Mathematics, Volume 79. 1989.

54. (with M. Hèbert and G.E. Weaver) * Two definability results in the equational context,* Proc. Amer. Math. Soc. ** 107** (1989), 47--53.

53. (with C. Bergman) * On the relationship of AP, RS, and CEP in congruence modular varieties, II,* Proc. Amer. Math. Soc. ** 103** (1988), 335--343.

52. The structure of finite algebras (with D. Hobby), American Mathematical Society, Contemporary Mathematics, Volume 76. 1988.

51. *Nilpotent and solvable radicals in locally finite congruence modular varieties,* Algebra Universalis ** 24** (1987), 251--266.

50. *Finite equational bases for congruence modular varieties,* Algebra Universalis ** 24** (1987), 224--250.

49. Algebras, Lattices, Varieties, I (with G. McNulty and W. Taylor). Wadsworth--Brooks/Cole, Monterey, California, 1987.

48. Commutator Theory for Congruence Modular Varieties (with R. Freese). London Mathematical Society Lecture Note 125. 1987.

47. Alfred Tarski: Collected Papers (edited with S. R. Givant, in four volumes). Birkhäuser, Basel-Boston-Stuttgart, 1986.

46. *The structure of finite algebras,* in: Atti degli Incontri di Logica Matematica vol.2 [Siena] (1985). pp. 561--584.

45. *Categorical quasivarieties revisited,* Algebra Universalis ** 19** (1984), 273--303.

44. (with J. Berman) * Clones satisfying the term condition,* Discrete Math. ** 52** (1984), 7--29.

43. *A new product of algebras and a type reduction theorem,* Algebra Universalis ** 18** (1984), 29--69.

42. (with B. Koppelberg and D. Monk) * Cardinality and cofinality of homomorphs of products of Boolean algebras,* Algebra Universalis ** 19** (1984), 38--44.

41. *A note on residually small varieties of semigroups,* Algebra Universalis ** 17** (1983), 143--149.

40. *Tame congruences,* in: Colloquia Mathematica Societatis Janos Bolyai, 43. Universal Algebra. Szeged [Hungary], 1983. pp. 293--305.

39. *The number of non-isomorphic models in quasi-varieties of semigroups,* Algebra Universalis ** 16** (1983), 195--203.

38. *Finite forbidden lattices,* in: Springer Lecture Notes 1004 (1983). Proceedings of the 4th International Conference on Universal Algebra and Lattice Theory [Puebla, Mexico, 1982]. pp. 176--205.

37. (with D. Monk) * Chains in Boolean algebras,* Annals Math. Logic ** 22** (1982), 137--175.

36. *Subdirect powers of non-Abelian groups,* Houston J. Math. ** 8** (1982), 389--399.

35. (with J. Baldwin) * Counting models in universal Horn classes,* Algebra Universalis ** 15** (1982), 359--384.

34. *Narrowness implies uniformity,* Algebra Universalis ** 15** (1982), 67--85.

33. *Residually small varieties of ***K***-algebras,* Algebra Universalis ** 14** (1982), 181--196.

32. (with B. Jónsson) * Powers of partially ordered sets: cancellation and refinement properties,* Math. Scand. ** 51** (1982), 87--120.

31. (with R. Quackenbush) * The spectrum of a lattice-primal algebra,* Discrete Math. ** 35** (1981), 157--163.

30. (with C. Tsinakis) * On recovering a bounded distributive lattice from its endomorphism monoid,* Houston J. Math. ** 7** (1981), 525--529.

29. *Residually small varieties of semigroups,* Algebra Universalis ** 13** (1981), 171--201.

28. (with S. Burris) * Decidable varieties with modular congruence lattices,* Bull. Amer. Math. Soc. ** 4** (1981), 350--352.

27. Decidability and Boolean Representations (with S. Burris). Memoirs AMS ** 32** (1981), number 246.

26. (with R. Freese) * Residually small varieties with modular congruence lattices,* Trans. Amer. Math. Soc. **264** (1981), 419--430.

25. (with A. Romanowska) * Varieties of -distributive bisemilattices, in: Contributions to General Algebra, H. Kautschitsch, W.B. Muller, and W. Nobauer eds. Klagenfurt, Austria, 1979.*

24. *A finite algebra ***A*** with SP*(**A**)* not elementary,* Algebra Universalis ** 8** (1978), 5--7.

23. *Para primal varieties: a study of finite axiomatizability and definable principal congruences in locally finite varieties,* Algebra Universalis ** 8** (1978), 336--348.

22. (with V. Faber and R. Laver) * Coverings of groups by Abelian subgroups,* Canad. J. Math. ** 30** (1978), 933--945.

21. (with C. Bergman and Zs. Nagy) * How to cancel a linearly ordered exponent,* in: Colloquia Mathematica Societatis Janos Bolyai, 29. Universal Algebra. Esztergom [Hungary], 1977. pp. 87--93.

20. *Automorphism groups of denumerable Boolean algebras,* Canad. J. Math. ** 29** (1977), 466--471.

19. *On spectra, and the negative solution of the decision problem for identities having a finite nontrivial model,* J. Symbolic Logic ** 40** (1975), 186--196.

18. (with S. Shelah) * The cardinals of simple models for universal theories,* in: Proceedings of the Tarski Symposium, 1971. Volume 25 of Symposia in Pure Mathematics, American Mathematical Society. Providence, 1974. pp. 53--74.

17. (with J. Baumgartner, F. Galvin and R. Laver) * Game theoretic versions of partition relations, I,* in: Colloquia Mathematica Societatis Janos Bolyai, 10. Infinite and Finite Sets. Keszthely [Hungary], 1973. pp. 131--135.

16. (with D. Monk) * On automorphism groups of Boolean algebras,* in: Colloquia Mathematica Societatis Janos Bolyai, 10. Infinite and Finite Sets. Keszthely [Hungary], 1973. pp. 951--988.

15. *Some unsolved problems between lattice theory and equational logic,* in: Proceedings of the University of Houston Lattice Theory Conference, 1973. pp. 564--573.

14. *Equational bases and nonmodular lattice varieties,* Trans. Amer. Math. Soc. ** 174** (1972), 1--43.

13. (with R. J. Thompson) * An elementary construction of unsolvable word problems in group theory,* in: Proceedings of the Conference on Decision Problems in Group Theory, UC Irvine, 1969. North-Holland 1972. pp. 457--478.

12. *A method for obtaining refinement theorems, with an application to direct products of semigroups,* Algebra Universalis ** 2** (1972), 324--338.

11. (with J. Mycielski and D. Thompson) * On Boolean functions and connected sets,* Math. Systems Theory ** 5** (1971), 259--270.

10. *Aleph-1 incompactness of ***Z***,*Colloq. Math. ** 23** (1971), 199--202.

9. *Negative solution of the decision problem for sentences true in every subalgebra of *<*N,+*>*,* J. Symbolic Logic ** 36** (1971), 607--609.

8. *On semigroups whose proper subsemigroups have lesser power,* Algebra Universalis ** 1** (1971), 21--25.

7. *On elementary types of symmetric groups,* Algebra Universalis ** 1** (1971), 13--20.

6. *A note on subgroups of infinite symmetric groups,* Indag. Math. ** 33** (1971), 53--58.

5. *Definability in lattices of equational theories,* Annals Math. Logic ** 3** (1971), 197--237.

4. *Cardinal multiplication of structures with a reflexive relation,* Fund. Math. ** 70** (1971), 59--101.

3. *Equational bases for lattice theories,* Math. Scand. ** 27** (1970), 24--38.

2. *Representations of integral relation algebras,* Mich. Math. J. ** 17** (1970), 279--287.

1. *On finite groupoids and ***K***-prime algebras,* Trans. Amer. Math. Soc. ** 133** (1968), 115--129.

#### Conference Talks

Attended Workshop on The Constraint Satisfaction Property: Complexity and Approximability at Dagstuhl, Germany (November) (2012).

Invited talk at the Conference on Universal Algebra and Lattice Theory at University of Szeged, Hungary (June) (2012).

Invited talk at special session on Universal Algebra and Lattice Theory at the University of Hawaii (March) (2012).

Invited talk at the program on algebraic approach to constraint satisfaction problems at the Fields Institute, University of Toronto (title: Finitely related clones and algebras with cube-terms) (2011).

Invited talk at the Algebra Seminar at the University of Szeged, Hungary (title: Finitely related clones and algebras with cube-terms) (2011).

Invited talk at ''The 2nd International Conference on Order, Algebra, and Logics, in honor of Ralph McKenzie, Hiroakira Ono, and Andrzej Wrośki'' (title: ''The number of Malcev clones is countable, a Taylor term requires only four variables, and other remarkable products of the fusion of finite universal algebra and constraint satisfaction theory'') (2011).

Talk to the algebra seminar at LaTrobe University, Melbourne, Australia (2011).

Invited talk at ''Jardafest'' International Conference on Algebras and Lattices, Prague, June (title: ''Inherently finitely related algebras and sparse relational clones'') (2010).

Invited talk at BLAST conference, Boulder, June (title: ''Inherently finitely related algebras and sparse relational clones'') (2010).

KAM Mathematical Colloquium (invited lecture to the Faculty of Mathematics and Physics of Charles University, Prague on March 11, 2010).

Invited talk at algebra seminar, Charles University, Prague on March 8, 2010.

Invited talk at Nowy Sad Algebra Conference, August, 2009.

Invited talk at AMS meeting in Urbana, March [invited talk at special session] (2009).

Invited talk at University of Georgia, Athens (CS Department) October (2008).

Mini-conference in algebra and algorithms at Sam Houston State University, April 18 [invited talk] (2008).

Participated and gave talk at the Workshop on the Algebraic Approach to Constraint Satisfaction Problems at AIM, March 31 - April 4 (2008).

Conference on Algorithmic Complexity and Universal Algebra, Szeged, Hungary, July [was unable to participate or give talk due to health emergency in family] (2007).

Opening talk at the Shanks workshop conference on The Algebraic Approach to Constraint Satisfaction Problems, Vanderbilt, June (2007).

American Mathematical Society, winter meeting in New Orleans, January [invited talk at special session] (2007).

Mathematics Colloquium at University of Colorado, October (2006).

Grätzer-Schmidt Conference, Erdös Center, Budapest, June (2006).

American Mathematical Society, winter meeting in San Antonio, January [invited talk at special session] (2006).

Midsummer Combinatorial Workshop Conference, DIMATIA Center, Charles University, Prague, July (2005).

Novi Sad Algebraic Conference, Novi Sad, Serbia, July (2005).

Conference on Universal Algebra and Lattice Theory, Szeged, Hungary, July (2005).

American Mathematical Society meeting in Nashville, October [twenty minute talk at special session on semigroups] (2004).

Walter Taylor Conference in Boulder, August (2004).

Logic Colloquium 2004 in Torino, Italy, July (2004).

Winter Meeting of the Canadian Mathematical Society in Vancouver, December [hour talk at special session] (2003).

American Mathematical Society meeting in Boulder, October [hour talk at special session] (2003).

NATO Advanced Study Institute, at the Universite de Montreal, July [a five-lecture workshop] (2003).

Annual Meeting of the Association for Symbolic Logic at the University of Illinois in Chicago, June [plenary talk] (2003).

Alfred Tarski Lectures at UC Berkeley (March 31, April 2, April 4) (2003).

University of Puerto Rico, March (2003).

Universita di Siena, June [seminar lecture] (2002).

AMS-UMI First Joint International Meeting, Pisa, June [hour lecture at special session] (2002).

Mycielski Conference, Boulder, May (2002).

International Conference on Modern Algebra, Vanderbilt, May (2002).

Oxford University, Mathematical Institute, October [two invited lectures] (2001).

Czech-Slovak Summer School, September [three plenary lectures] (2001).

Tame Congruence Workshop Conference, Erdös Center, Budapest, first two weeks of July 2001 [chairman of the conference, presented six lectures] (2001).

University of Novi Sad, June [Colloquium] (2001).

Charles University, Prague, June [Colloquium] (2001).

University of Wroclaw, June [Colloquium] (2001).

Tarski Centenary Conference, Warsaw, May [plenary talk] (2001).

AMS Meeting at Columbia, South Carolina, March (2001).

Fried Conference, Budapest, August (1999).

University of Wroclaw, July [Colloquium] (1999).

Universal Algebra and Lattice Theory Conference, Szeged, Hungary, August (1998).

University of Wroclaw, June [Colloquium] (1998).

University of Dresden, June [Colloquium] (1998).

University of Potsdam, June [Colloquium] (1998).

AMS Meeting at Louisville, March [special session] (1998).

International Congress in Algebras and Combinatorics, Hong Kong (1997).

Joint Mathematics Meeting, Pretoria, South Africa, June [hour talk at special session] (1997).

University of Capetown, South Africa, June [Colloquium] (1997).

International Conference on Modern Algebra and its Applications, Vanderbilt, May [plenary lecture] (1996).

University of Brisbane [twenty seminar talks] (1995).

University of Hawaii [Colloquium] (1995).

Magari Conference, Siena, Italy, April [plenary lecture] (1994).

Institut d'Estudis Catalans, Centre de Recerca Matemática, Barcelona, May [five lectures] (1994).

University of Nebraska [Colloquium] (1994).

UC Berkeley [Logic Colloquium] (1994).

Vanderbilt University, December [Colloquium] (1993).

Universal Algebras and Categories, MSRI, July [co-chair of the two-week workshop, presented one hour lecture] (1993).

Evelyn Nelson Lecture, McMaster University, Ontario, March (1993).

Pontifica Universidad Catolica de Santiago, Chile, February [six seminar talks] (1993).

UC Berkeley [Colloquium] (1992).

Alan Day Conference, McMaster University, Ontario (1992).

University of Colorado [Colloquium] (1990).

Summer Meeting of Canadian Math. Society, Halifax [plenary lecture] (1990).

Jónsson Symposium, Iceland [plenary lecture] (1990).

Victoria University, Wellington NZ [Colloquium] (1989).

University of Canterbury, Christchurch NZ [Colloquium] (1989).

Third International Conference on the Theory of Groups and Related Topics, Canberra [plenary lecture] (1989).

Maltsev Conference, Novosibirsk [plenary lecture] (1989).

Royal Melbourne Inst. Tech. [Colloquium] (1989).

Victoria Algebra Conference, Melbourne (1989).

Waterloo University [Colloquium] (1989).

University of Manitoba [seminar talk] (1988).

Technische Hochschule Darmstadt [seminar talks] (1988).

Math. Inst. Hungarian Acad. Sci, Budapest [several seminar talks] (1988).

International Conference on Algebra, Lisbon, Portugal (1988).

UC Berkeley [Logic Colloquium] (1987).

Conference on Algebra, Lattices, Logic, Asilomar (1987).

Harvey Mudd College, Claremont [Colloquium] (1987).

UC Riverside [Colloquium] (1987).

University of South Carolina [Colloquium and seminar talks] (1987).

The Citadel, Charleston (1987).

17th International Conference on Multiple-Valued Logic, Boston (1987).

University of Massachussetts, Amherst [Colloquium] (1987).

Second Molokai Conference, Hawaii (1987).

Fine Structure Conference, Berkeley [fourteen lectures] (1986).

Chico State University [Colloquium] (1986).

Simon Fraser University, Vancouver [Colloquium and seminar talks] (1986).

UC Berkeley [Logic Colloquium] (1985).

University of Calgary [seminar talk] (1985).

Iowa State University, Ames [Colloquium] (1985).

Conference on UA & LT, at The Citadel, Charleston, SC (1984).

University of Siena, Italy [three-week course] (1984).

University of Siena, Italy [four talks at a conference] (1984).

First Molokai Conference, Hawaii [two talks] (1984).

University of Hawaii [fifteen weeks of seminar talks] (1984).

Workshop on UA & LT, Szeged, Hungary (1983).

Charles University, Prague [Colloquium] (1983).

Waterloo University [seminar talks] (1983).

University of Colorado [seminar talks] (1983).

Vanderbilt University [one week of seminar talks] (1983).

International Conference on UA & LT, Puebla, Mexico [one week of lectures] (1982).

UC Berkeley [Logic Colloquium] (1982).

Jónsson Symposium, Vanderbilt University (1981).

University of Colorado [Colloquium] (1980).

AMS Special Session on UA & LT at University of Colorado (1980).

UC Berkeley [Logic Colloquium] (1980).

University of Hawaii [Colloquium and seminar talks] (1979).

Conference on Universal Algebra, Claremont (1978).

E.T.H., Zürich (1978).

Math. Inst. Hungarian Acad. Sci., Budapest (1978).

East-West Conference on Universal Algebra, Klagenfurt (1978).

Freie University, Berlin (1978).

University of Freiburg (1978).

University of Kassel (1978).

Technische Hochschule Darmstadt (1978).

Semester on Algebra at Banach Center, Warsaw [six lectures] (1978).

Vanderbilt University [seminar talks] (1977).

University of Calgary [Colloquium] (1975).

AMS Special Session on Game Theory, Washington, DC (1975).

UCLA [Logic Colloquium] (1975).

University of Washington [Colloquium] (1974).

UCLA [Logic Colloquium] (1973).

AMS Special Session on Lattice Theory, Houston (1973).

Erdös Symposium, Hungary (1973).

SUNY at Buffalo (1972).

Waterloo University [Colloquium and seminar talks] (1972).

University of Manitoba [Colloquium] (1972).

Tarski Symposium, Berkeley (1971).

McMaster University, Ontario [Colloquium] (1971).

AMS Summer Regional Conference at Pennsylvania State U. (1969).

Vanderbilt University [Colloquium] (1969).

UC Berkeley [Logic Colloquium] (1969).

Oberwolfach Conference (1968).

UC Berkeley [Logic Colloquium] (1967).

#### Awards

Alfred Tarski Lectures - University of California, Berkeley (2003)

Fulbright Scholar Program - Senior Scholar Award (Fall 1989)

Sloan Foundation Fellowship (1973-1975)