Updated: June 1992

1. Name: MEKLER, Alan Harvey

2. Department: Mathematics & Statistics

3. Date of Birth: 28 October 1947

4. Current Rank: Professor

5. Current Contract: (X) Tenured



Degrees College/University/Institution Field of Study Year

B.A. York University, Toronto Mathematics 1969

M.A. York University, Toronto Mathematics 1970

M.Sc. Stanford University, California Mathematics 1971

Ph.D. Stanford University, California Mathematics 1976



Position held Dates Department and Institution

Research Associate 1976-78 Math, Carleton University

Lecturer 1978-79 Math, University of Toronto

Visiting Assistant Professor 1979-80 Math, Univ of Western Ontario

Wissenschaft-Mitarbeiter 6/80-9/80 Math, Universitat Essen Assistant Professor 9/80-12/80 Math, Auburn University

Assistant Professor 12/80-8/83 Math, Simon Fraser University NSERC Research Fellow

Associate Professor 9/83-1986 Math, Simon Fraser University NSERC Research Fellow

Professor 1986-present Math, Simon Fraser University

Visiting Professor Jan-Apr 1989 The Hebrew University, Jerusalem

Member 1989-90 Mathematical Sciences Research Institute



Applications of set theory to algebra, stationary logic, abstract model theory.



Canadian Mathematical Society

Association for Symbolic Logic

American Mathematical Society



(Listed serially with dates and full details. Most recent listed last).

Doctoral Fellowship, The Canada Council


11. RECORD OF RESEARCH FUNDING: Please list only those monies in a given year which have been, or will be, received during the fiscal year April 1 to March 31. Please list the title of the award, the source and the type of award, and the date and duration of the award. If it is a joint award, please list the co-investigators.


NSERC Operating Grant 1980-81 $ 3,500 Applications of model theory and theory and set theory to algebra

NSERC Operating Grant 1981-82 $ 5,300 Applications of model theory and set theory to algebra

NSERC Operating Grant 1982-83 $ 6,112 As above.

NSERC Operating Grant 1983-84 $10,600 As above.

NSERC Operating Grant 1984-85 $11,130 As above.

NSERC Operating Grant 1985-86 $17,856 As above.

NSERC Operating Grant 1986-87 $17,856 As above.

NSERC Operating Grant 1987-88 $17,856 As above.

NSERC Operating Grant 1988-89 $24,840 As above.

NSERC Operating Grant 1989-90 $24,840 As above.

NSERC Operating Grant 1990-91 $24,840 As above.

NSERC Operating Grant 1991-92 $35,000 As above.


12. RECORD OF FULL-TIME PERSONNEL: Please list those individuals who are full-time under your supervision, i.e. PDF's, Technicians, Research Associates, Research Assistants. Please list the title of the position, the date of appointment, highest degree or technical qualification, and the source of funds which supports them.

Please list in order: PDF's, Research Associates, Research Assistants and Technicians


Mr. G. Schlitt (B.Sc.) - Research Assistant - Summer 1985/Fall 1985

(Supported by NSERC grant)

Dr. G. Srour - Postdoctoral Fellow - 1985/86. (Supported by NSERC grant)

M. Gilchrist - Summer 1986, Summer 1987.

R. Lapsley - Summer 1988

M. Gilchrist - Summer 1988, Fall, 1989.

G. Schlitt - 1990 - Postdoctoral Fellow


13. RECORD OF INVITED TALKS: (At meetings, at other universities, or

at research establishments.) Please give the date, the title of the talk,

and the name and address of the organization to which the talk was


1976 The number of k-free Abelian groups and the size of Ext, Bicentennnial Abelian Group Theory Conference, Las Cruces, New Mexico.

1978 Almost free groups, York University, Toronto.

1980 Applications of logic to algebra, Universitat Essen, Essen, Germany.

1981 L(Q) may have the Weak Beth property, Bedford College, London, England.

1981 Stationary Logic of Ordinals, Institute for Advanced Studies, The Hebrew University, Jerusalem, Israel.

1982 Beyond First Order Logic, University of California, Irvine, California.

1982 Categoricity results for Low -free algebras, Special Session on Model Theory, American Mathematical Society, College Park, Maryland.

1982 Structure of ?1-separable groups, Abelian Group Theory Conference, Honolulu, Hawaii.

1982 Finitely additive measures on N , York University, Toronto.

1982 Structure of ?1-separable groups, Kobe University, Kobe, Japan.

1983 Categoricity results for Low -free algebras, University of Waterloo.

1983 Set theory and structure theory for Abelian groups, Universitat Freiburg.

1983 Almost free algebras, Mathematics Colloquium Zurich (ETH & Universitat Zurich).

1983 Finitely additive measures on N , Special Session on Logic, Canadian Math. Soc. Summer Meeting, Vancouver.

1984 A lawless order, Mathematics Colloquium, University of California, Irvine.

1984 Groups embeddable in the homeomorphisms of Q. Dalhousie University (Colloquium).

1984 Stability of nilpotent groups, Forking Festival, University ofIllinois, Chicago.

1984 Lawless Order, Special year in Logic, University of Maryland,College Park, Maryland.

1984 Classification theory and stationary logic, Mid-AtlanticMathematical Logic Seminar. Princeton University, Princeton, New Jersey.

1985 The Solution to Crawley's Problem, Abelian Group Theory Meeting at Oberwolfach, Oberwolfach, West Germany.

1985 Almost Free Algebras, Marquette University, Milwaukee, Wisconsin. (Colloquium).

1985 Reflexive Abelian Groups, Marquette University, Milwaukee, Wisconsin (Algebra Seminar).

1985 Groups embeddable in the homeomorphisms of Q. Rutgers University (Logic Seminar).

1985 Classification theory and stationary logic. Conference on Classification Theory, University of Illinois, Chicago, Illinois.

1986 Almost Free Algebras, Conference on Model Theory. Model Theoretic Algebra and Models of Arithmetic, University of Notre Dame, Notre Dame, Indiana.

1986 The structure of dual groups, University of Colorado, Colorado Spring, Colorado (Colloquium).

1986 Abelian groups of the form Hom (A, Z ), Mid-Atlantic MathematicalLogic Seminar. Rutgers University, New Brunswick, New Jersey.

1986 Uncountable Abelian groups. Wesleyan University, Middletown, Connecticut (Colloquium).

1986 Almost free algebras, McMaster University, Hamilton, Ontario (Algebra Seminar).

1986 Almost free algebras, Bowling Green State University, Bowling Green, Ohio (Colloquium).

1986 Almost free algebras, University of Calgary, Calgary, Alberta, (Combinatorics Seminar).

1986 Uncountable Abelian groups, University of Calgary, Calgary, Alberta (Colloquium).

1987 Dual groups, Set Theory and its Applications Conference at York,York University, Toronto

1988 Almost Free Groups, London Mathematical Society Seminar, Durham(July), U.K.

1988 Almost Free Algebras, Helsinki University (July).

1988 Low-free algebras, Connecticut Logic Seminar, Yale University, NewHaven, Connecticut.

1989 Almost free algebras, University California, Irvine.

1989 Almost free modules, Abelian Group theory meeting, Oberwolfach, Germany.

1989 Set theoretic methods in algebra, Logic Club, University of California, Berkeley.

1989 Sequences of dual groups, Mid-Atlantic Model theory, Seminar, Berkeley.

1989 Set theoretic methods in abelian group theory, University of California, Davis.

1989 Sequences of dual groups, Special Session in Model Theory, CMS Winter Meeting.

1990 Mathematics for the Sauna, Midwest Model Theory Meeting, University of Wisconsin, Parkside.

1990 Almost Free Algebras: 20 years of progress, ASL Summer meeting

1990: Logic Colloquium '90, Helsinki (Invited speaker).

1990 Dual Groups: Department of Maths, University of Melbourne,Melbourne, Australia.

1990 Groups and long Ehrenfeucht-Fraisse games, Special Session on Interactions of Logic and Group Theory, A.M.S. Meeting, Irvine, California.

1991 Homogeneous Posets, NATO Meeting on Finite and Infinite Combinatorics, Banff, Alberta (Invited speaker).


14. RECORD OF PROFESSIONAL DISTINCTION: (e.g. serving on a review

panel for a government or granting agency; serving on advisory committee

for government meeting; serving as an officer of a professional society).


Executive Committee, Institute of Applied Logic

Board of Directors, Canadian Math. Society, 1986-91, Nominating

Committee 1989-91.

Grant Selection Committee, NSERC 1989-91

Editor, CJM and CBM 1992 -



UNIVERSITY Give the full name of the committee (Departmental, Faculty,

Senate, University). If possible, specify the semesters involved and any

special position held (e.g. Chairman).

i) Departmental Committees:

Undergraduate Studies Committee (1981-82)

Colloquium Chairman (1982-1986)

Co-ordinator for Mathematical Logic Seminar (1981-)

Graduate Studies (1990-)

DTC (1991-92)


ii) Faculty Committees:


iii) University Committees:






(a) Please list the students who have completed a thesis under you, as Senior Supervisor:


Student's Name Degree Date of Completion Thesis Title

Laflamme, C. M.Sc. Summer 1983 Structure of Nonstandard

Number Systems

Schlitt, G. M.Sc. Summer 1986 Some results on


Lapsley, R. M.Sc. Summer 1990 Trees, Orders and Forcing


(b) Please list those students who are currently working on a degree under you, as Senior Supervisor:

Student's Name Degree Semester Student Began Degree

Status: Active, On Leave, Other

Gilchrist, M. Ph.D. 1985-3 Active



Supervisor), and the degree for which the student is enrolled.

Student's Name Degree for which Enrolled

Yi, X. Ph.D.

Gilchrist, M. Ph.D.

Szpitun, L. Ph.D.

Schipperus, R. M.Sc.

19. TEACHING AND RESEARCH RECORD: (For each teaching semester, please

list each course taught together with its calendar descriptor and title.

Please make a note of any special teaching assignments and/or requirements.

Please indicate any semesters which were used for sabbatical leave,

administrative leave, leaves of absence, or for any other special purpose.)

Semester Course Descriptor and Title Comments

81-1 252-3 Calculus IV

81-2 - Teaching Semester

81-3 808-4 Mathematical Logic III

82-1 144-3 Intro. to Pure Math.

82-2 Research

82-3 Teaching Semester

83-1 807-4 Math Logic: Selected Topics

83-2 Research

83-3 808-4 Mathematical Logic III

84-1 Research

84-2 452-3 Set Theory

84-2 251-3 Calculus III

84-3 Research

85-1 426-3 Intro. to Lebesgue Theory

85-1 306-3(1) Formal Languages and Automata

with Applications

85-2 Research

85-3 438-3(1) Linear Algebra

86-1 807-4 Math. Logic: Selected Topics

86-1 308-3 Linear Programming

86-2 Research

86-3 Research

87-1 800-4 Pure Math: Selected Topics

87-2 451-3(1) Mathematical Logic

87-2 438-3 Linear Algebra

87-3 831-4 Real Analysis 1

87-3 438-3 Linear Algebra

87-3 GSS-1

88-1 812-4 Algebra 1

88-2 Research

88-3 144.3 Intro. to Pure Math.

88-3 300-3 Intro. to Formal Languages and

Automata with Applications

89-1 Sabbatical

89-2 Sabbatical

89-3 Sabbatical

90-1 440-3 Galois Theory

90-1 242-3 Introduction to Analysis

90-2 Research

90-3 438-3 Linear Algebra

91-1 444-3 Topology

91-2 Research


20. PUBLICATION LIST: Please list in time order (last paper last) only refereed papers. Use the format - full authorship, the title, the name and volume of the journal or the equivalent information if the article appeared in a book, first and last page numbers and the year. The authorship format should be identical to that in the original publication. Please also list work which have been accepted for publication.


1. Mekler, A.H., Theories with models of prescribed cardinalities, J. of Symbolic Logic 42, (1977), 251-253.

2. Mekler, A.H., The size of epimorphic extensions, Algebra Universalis 8, (1978), 228-232.

3. Mekler, A.H., The number of k-free groups and the size of ext, in Abelian Group Theory, Springer-Verlag Lecture Notes in Mathematics, No. 616, (1977), 323-331.

4. Mekler, A.H., Model Complete theories with a distinguished sub-structure, Proc. Amer. Math. Soc. 75, (1979), 294-299.

5. Mekler, A.H., On residual properties, Proc. Amer. Math. Soc. 78, (1980), 187-188.

6. Mekler, A.H., How to construct almost free groups, Canad. J. Math. 32, (1980), 1206-1228.

7. Eklof, P.C., and Mekler, A.H., On constructing indecomposable groups in L, J. Algebra 49, (1977), 96-103.

8. Eklof, P.C., and Mekler, A.H., Infinitary stationary logic and Abelian groups, Fund. Math. CXII, (1981), 1-15.

9. Eklof, P.C., and Mekler, A.H., Stationary logic of finitely determinate structures, Ann. Math. Logic 17, (1980), 227-269 .

10. Mekler, A.H., Stability of nilpotent groups of class 2 and prime exponent, J. of Symbolic Logic 46, (1981), 781-788.

11. Herre, H., Smith, Kenneth, W., and Mekler, A.H., Superstable graphs, Fund. Math. CXVIII, (1983), 75079.

12. Mekler, A.H., On Shelah's Whitehead groups and CH, Rocky Mountain J. Math. 12, (1982), 271-278.

13. Mekler, A.H., 1-separable groups of mixed type, in Abelian Group Theory, Springer-Verlag Lecture Notes in Math. No. 874, (1981), 114-126.

14. Mekler, A.H., Primitive rings are not definable in Loo, Comm. Alg., 10, (1982), 1689-1690 .

15. van den Dries, L.P.D., Glass, A.M.W., MacIntyre, A., Mekler, A.H. and Poland, J., Elementary equivalence and the commutator subgroup Glasgow Math. J. 23, (1982), 115-117.

16. Mekler, A.H., Pelletier, D., and Taylor, A., A note on a lemma of Shelah concerning stationary sets, Proc. Amer. Math. Soc., 82, (1981), 764-768.

17. Eklof, P.C., Mekler, A.H. and Shelah, S., Almost disjoint Abelian groups, Israel J. Math. 49 (1984), 34-54.

18. Mekler, A.H. and Shelah, S., Stationary logic and its friends I, Notre Dame J. Formal Logic, 26, No. 2 (1985), 129-138.

19. Mekler, A.H., Stationary logic of ordinals, Annals of Pure and Applied Logic 26, (1984) 47-68.

20. Mekler, A.H., c.c.c. forcing without combinatorics, J. Symbolic Logic 49 (1984), 830-832.

21. Eklof, P.C., and Mekler, A.H., On endomorphism rings of w1-separable primary groups. Abelian Group Theory, Springer-Verlag Lecture Notes in Mathematics No. 1006 (1983), 320-339.

22. Mekler, A.H., Proper forcing and Abelian groups, Abelian Group Theory, Springer-Verlag Lecture Notes in Mathematics No. 1006 (1983), 285-303.

23. Mekler, A.H., Finitely additive measures on N and the additive property, Proc. Amer. Math. Soc. 92 (1984), 439-444.

24. Holland, W.C., Mekler, A.H., and Shelah, S., Lawless order, Order 1, (1985), 383-397.

25. Mekler, A.H. and Shelah, S., Stationary logic and its friends II, Notre Dame J. Formal Logic. 27, No. 1 (1986) 39-50.

26. Holland, W.C., Mekler, A.H. and Shelah, S., Total orders whose carried groups satisfy no laws, proceedings of the First International Symposium on Ordered Algebraic Structures. Luminy-Marseilles 1984. Heldeman Verlag Berlin (1986) 29-33.

27. Mekler, A.H., and Shelah, S., w-elongations and Crawley's Problem. Pacific J. Math. 121, No. 1 (1986), 121-132.

28. Mekler, A.H. and Shelah, S., The Solution to Crawley's Problem, Pacific J. Math. 121, No. 1 (1986), 133-134.

29. Mekler, A.H. and Shelah, S., When k-free to implies strongly k-free, Abelian Group Theory, Gordon and Breach (1987) 137-148.

30. Mekler, A.H., Groups embeddable in the autohomeomorphisms of Q, J. London Math. Society (2) 33 (1986) 49-58.

31. Mekler, A.H., Classification Theory and Stationary Logic, Canadian J. Math. 39, No. 4, (1987) 893-907.

32. Holland, W.C., Mekler, A.H., and Reilly, N.R., Varieties of Lattice Ordered Groups in which Prime Powers Commute, Algebra Universalis. 23 (1986), 196-214.

33. Mekler, A.H. and Nelson, E.M., Equational Bases of "If-Then-Else", SIAM J. Compute., 16 (1987), 465-485.

34. Eklof, P.C., Mekler, A.H., Shelah, S., On Strongly-Non-Reflexive Groups, Israel J. Math., 59 (1987), 283-298.

35. Mekler, A.H., The structure of groups which are almost the direct sum of countable Abelian Groups, Trans. Amer. Math. Soc. 303, No. 1, (1987), 145-160.

36. Eklof, P.C. and Mekler, A.H., Categoricity Results for Lok-free Algebras, Annals of Pure and Applied Logic, 37 (1988), 81-99.

37. Eklof, P.C., Huber, M., Mekler, A.H., Totally Crawley Groups, J. of Algebra, 112 (1988), 370-384.

38. Adamek, J., Mekler, A.H., Nelson, E., Reiterman, J., On the logic of continuous algebras, Notre Dame J. Formal Logic. 29 (1988), 365-380.

39. Mekler, A.H. and Shelah, S., Diamond and l-systems. Fundamenta Mathematica, 131 (1988), 46-51.

40. Mekler, A.H. and Shelah, S., Uniformization Principles, J. Symbolic Logic, Vol. 54, No. 2, (1989), 441-459.

41. Komjath, P., Mekler, A.H., Pach, J., Some universal graphs, Israel Math. J., Vol.64, No.2, (1988), 158-168.

42. Mekler, A.H. and Shelah, S., Low-free algebras, Algebra Universalis, Algebra Universalis, 26 (1989) 351-366.

43. Mekler, A.H. and Shelah, S., The consistency strength of "every stationary set reflects", Israel J. Math, Vol. 67, No.3, (1989) 353-366.

44. Mekler, A.H., Universal structures in Power ?1, J. Symbolic Logic. 55 (1990) 466-477.

45. Macpherson, D., Mekler, A.H., and Shelah, S., The number of infinite substructures. Proc. Cambridge Phil. Soc., 109 (1991) 109-209.

46. Mekler, A.H. and Shelah, S., Determining Abelian p-groups from their n-Socles (Communications in Algebra). 181 (1990) 287-307.

47. Mekler, A.H., Almost Free Groups in Varieties. J. of Algebra. Vol. 145, No.1 (1992) 128-142.

48. Mekler, A.H., E. Nelson and S. Shelah, A variety with solvable but not uniformly solvable word problem, London Math. Soc. (To appear)

49. Mekler, A.H., Rubin, M. and Steinhorn, C., Dedekind completeness and the algebraic complexity of O-minimal structures. Can. J. Math. (To appear)

50. Mekler, A.H., Shelah, S., Every coseparable group may be free. Israel J. Math.

51. Mekler, A.H., Homogeneous partially ordered sets, Conference on Finite and Infinite Combinatorics in Sets and Logic.

52. Covington, J., Macpherson, D. and Mekler, A., Stabilisers of ideals and infinite symmetric groups, J. Aust. Math. Soc.(Accepted 1992).

53. Mekler, Alan H. and Shelah, S., The canary tree, Canadian Bull. Math.(Accepted 1992).

54. Mekler, Alan H. and Covington, J. Stabilizers of trivial ideals, Bulletin London Mathematical Society. (Accepted 1992).

55. Eklof, Paul C. and Mekler, Alan H., Almost Free Modules. Set-theoretic methods, Book Reviews, Bull A.M.S. (reviewer Lazlo Fuchs) (Accepted 1992).



1. Eklof, P.C. and Mekler, A.H., Almost Free Modules: Set TheoreticMethods, North Holland, 1990 (481 pages) (about 90 pages consist of results which are being published for the first time.)


1. Mekler, A.H., Shelah, S., Compactness results for isomorphism quantifiers. Annals of Math.

2. Mekler, A.H., Shelah, S. and Vaananen, J., The Ehrenfeucht-Fraisse-game of length w1, Trans. Amer. Math. Soc.

3. Covington, J. and Mekler, A., Subgroups of infinite symmetric groups which are full for large sets, J. of Algebra.

4. Eklof, Paul C., Mekler, A. and Shelah, S., On coherent systems of projections for ?1 - separable groups, Comm. Alg.

5. Mekler, A., Schipperus, R., Shelah, S. and Truss, J.K., The Non-embeddability of AAut G into the homeomorphism group of the rationals.

6. Mekler, A.H., Scattered Subsets of Q.

7. Mekler, A., Nelson, E. and Shelah, S., A Variety with Solvable, but not Uniformly Solvable, Word Problem, London Mathematical Society.

8. Mekler, A., Schipperus, R., Shelah, S., The Random Graph and Automorphisms of the Rational World, AMS.


1. Appendix to "Incompactness in Regular Cardinals" by S. Shelah Notre Dame J. Formal Logic, 26 (1985), 195-228.

2. How hard is the word problem in free lattice ordered groups? Abstracts of the AMS (1984) 84T-06-175 p. 203.

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