Publications - G. Cherlin

Gregory Cherlin, Publication List; less recent

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Recent publications | In preparation

Older publications:

99. Small representations of SL2 in the finite Morley rank category,
with A. Deloro.

J. Symb. Logic 77 (2012), 919-933.

98. Two problems on homogeneous structures, revisited

in Model Theoretic Methods in Finite Combinatorics, M. Grohe and J.A. Makowsky eds.,

Contemporary Mathematics, 558, American Mathematical Society, 2011.

97. Forbidden Substructures and Combinatorial Dichotomies: WQO and Universality

Discrete Mathematics 311 (2011), 1543-1584

doi 10.1016/j.disc.2011.03.014

Additional Reference:
Jens Gustedt. Finiteness theorems for graphs and posets obtained by compositions,
Order 15 (1998/99), 203-220.

96. Semisimple torsion in groups of finite Morley rank,
with J. Burdges

J. Math. Logic 9 (2009), 183-200.

95. Simple Groups of Finite Morley Rank of Even Type,
with T. Altınel and A. Borovik,

Mathematical Surveys and Monographs, 145,
American Mathematical Society, Providence, RI, 2008
xx+556 pp.

94. A generation theorem for groups of finite Morley rank,
with J. Burdges,

J. Math. Log. 8 (2008), 163–195.

93. Genericity, Generosity, and Tori,

Journal of the Inst. of Math. Jussieu, 7 (2008), 705-722.

92. Permutation groups of finite Morley rank,
with A. Borovik

pp. 59-124, in Model Theory with Applications to Algebra and Analysis, Vol. 2,
Zoé Chatzidakis, Dugald Macpherson, Anand Pillay, and Alex Wilkie, eds.,
London Mathematical Society Lecture Note Series, Cambridge University Press, 2008.

91. Simple groups of finite Morley rank of unipotent type,
with A. Borovik and J. Burdges.

pp. 47-62, in Algebra, Logic, Set Theory. Festschrift fuer Ulrich Felgner zum 65. Geburtstag, B. Loewe ed.,
Studies in Logic, College Publications at Kings College London, 2007.

90. Involutions in groups of finite Morley rank of degenerate type,
with J. Burdges and A. Borovik,

Selecta Mathematica, 13 (2007) 1-22.

89. A generic identification theorem for L^*-groups of finite Morley rank
with A. Berkman, A. Borovik, and J. Burdges,

J. Algebra, 319 (2008), 50-76.

88. Universal graphs with a forbidden subtree,
with S. Shelah,

J. Comb. Theory, Series B, 97 (2007), 293-333.

87. Universal graphs with a forbidden near-path or 2-bouquet,
with L. Tallgren,

J. Graph Theory, 56 (2007), 41-63. © Wiley.

86. Minimal connected simple groups of finite Morley rank with strongly embedded subgroups,
with J. Burdges and E. Jaligot,

J. Algebra 314 (2007), 581-612.

85. Good tori in groups of finite Morley rank,

J. Group Theory 8 (2005), 613-621.

84. A note on orthogonality and stable embeddedness,
with E. Hrushovski and M. Djordjevic,

J. Symb. Logic 70 (2005), 1359-1364.

83. Categoricity in power n+2,

Discrete Mathematics 291 (2005), 55-71.

82. Locally finite generalized quadrangles with at most 5 points per line,

Discrete Mathematics 291 (2005), 73-79.

81. Simple groups of finite Morley rank, 2002

in Proceedings of Euroconference on Model Theory and its Applications,
Belair, Chatzidakis, d'Aquino, Marker, Otero, Point, Wilkie, eds.,
Quaderni di Matematica 11 (2005), 41-72.

80. Limoncello,
with T. Altınel.

J. Algebra, 291 (2005), 371-413.

79. Simple L^*-groups of even type with weakly embedded subgroups,
with T. Altınel.

J. Algebra, 286 (2005), 76-106.

78. Simple L^*-groups of even type with strongly embedded subgroups,
with T. Altınel.

J. Algebra 272 (2004), 95-127.

77. Tame minimal simple groups of finite Morley rank,
with E. Jaligot,

J. Algebra 276 (2004), 13-79.

76. Parabolic 2-local subgroups in groups of finite Morley rank of even type,
with T. Altınel, A. Borovik, and L.-J. Corredor,

J. Algebra 269 (2003), 250-262.

75. Classification of simple K*-groups of finite Morley rank and of even type: geometric aspects,
with T. Altınel and A. Borovik,

Groups, combinatorics, and geometry (Durham 2001), 1-12, World Sci. Publishing, River Edge NJ, 2003.

74. On groups of Finite Morley Rank of Even Type,
with T. Altınel,

J. Algebra 264 (2003), 155-185.

73. Borovik-Poizat rank and stability,
with J. Burdges,

J. Symb. Logic, 67 (2002), 1570-1578.

72. Pushing up and C(G,T) in groups of finite Morley rank of even type

With T. Altınel and A. Borovik.

J. Algebra 247 (2002), 541-576.

71. Two cardinal properties of homogeneous graphs, with S. Thomas.

J. Symb. Logic, 67 (2002), 217-220.

Erratum. See p.2, and reference [Ack]. File updated 2022.

70. Finite structures with few types, with E. Hrushovski, Annals of Mathematics Studies, PUP, Princeton, 193 pp., January 2003.
Additional notes (2/2004).
69. Forbidden subgraphs and forbidden substructures,
with N. Shi,

J. Symb. Logic 66 (2001), 1342-1352.

68. Minimal antichains in well-founded quasi-orders with an application to tournaments,
with B. Latka

J. Combinatorial Theory Series B. 80 (2000), 258-276. `

67. Groups of finite Morley rank and even type with strongly closed abelian subgroups,
with T. Altınel and A. Borovik,

J. Algebra 232 (2000), 420-461.

66. The classification of finite homogeneous groups,
with U. Felgner,

J. London Math. Society 62 (2000), 784-794.

65. Sporadic homogeneous structures,

The Gelfand Mathematical Seminars, 1996-1999, pp. 15-48, Birkhäuser, 2000.

64. Infinite imprimitive homogeneous 3-edge-colored complete graphs,

J. Symb. Logic 64 (1999), 159-179.

63. Central extensions of algebraic groups of finite Morley rank,
with T. Altınel,

J. Symb. Logic 64 (1999), 68-74.

62. On groups of finite Morley rank with weakly embedded subgroups,
with T. Altınel and A. Borovik,

J. Algebra 211 (1999), 409-456.

61. A Hall theorem for ω-stable groups,
with T. Altınel, L.-J. Corredor, and A. Nesin,

J. London Math. Soc. 57 (1998), 385-397.

60. Universal graphs with forbidden subgraphs and algebraic closure,
with S. Shelah and N. Shi,

Advances in Applied Mathematics 22 (1999), 454-491.

59. Groups of mixed type,
with T. Altınel and A. Borovik,

J. Algebra 192 (1997), 524-571.

58. Graphs omitting a bushy tree,
with N. Shi and L. Tallgren

J. Graph Theory 26 (1997), 203-210.

57. Graphs omitting sums of complete graphs,
with N. Shi,

J. Graph Theory 24 (1997), 237-247.

56. Graphs omitting a finite set of cycles,
with N. Shi,

J. Graph Theory 21 (1997), 351-355.
MR 96k:05106.

55. Large finite structures with few types,

In Algebraic Model Theory, B. Hart, A. H. Lachlan, and M. Valeriote, eds.,
Proceedings of a NATO Instructional Conference, Toronto, 1996, pp. 53-105.
Kluwer Academic Publishers, 1997.

54. Arities of permutation groups: wreath products and k-sets,
with G. Martin and D. Saracino,

J. Combinatorial Theory Series A 74 (1996), 249-286. MR 97c:20001.

See also:
Dan Saracino,

On a combinatorial problem from the model theory of wreath products. I, II.
J. Combin. Theory Ser. A 86 (1999), no. 2, 281--305, 306--322.
MR1685534
On a combinatorial problem from the model theory of wreath products. III.
J. Combin. Theory Ser. A 89 (2000), no. 2, 231--269.
MR1741014

53.

There is no universal countable pentagon-free graph,
with P. Komjáth,

J. Graph Theory 18 (1994), 337-341. MR 95c:05072.

See also paper 56 and the theorem of Füredi-Komjáth that deals with arbitrary 2-connected graphs which are not complete.
Z. F¨redi and P. Komjáth, On the existence of countable universal graphs.
J. Graph Theory 25 (1997), no. 1, 53-58. MR1441978

52. An integer lattice arising in the model theory of wreath products,
with Gary Martin,

in Logical Methods: In Honor of Anil Nerode's Sixtieth Birthday,
Progress in Computer Science 12, J. N. Crossley et al, eds., Birkhäuser, Boston, 1993, 178-193.
MR 95i:03071.

51. Homogeneous directed graphs,

in Finite and infinite combinatorics in sets and logic (Banff, 1991),
NATO ASI Ser. C, Math. Phys. Sci., 411, Kluwer, Dordrecht, 1993.
MR 94m:05092.

50. The Classification of Countable Homogeneous Directed Graphs and Countable Homogeneous n-Tournaments,

AMS Memoir 131 Number 621, January 1998, xi+161pp. AMS, Rhode Island.

49. On homogeneous nilpotent groups and rings,
with D. Saracino and C. Wood,

Proceedings American Math. Society 119 (1993), 1289-1306. MR 94a:03059.

48. Combinatorial problems connected with finite homogeneity,

in Proceedings of the Novosibirsk Conference on Model Theory and Algebra (1989),
Contemporary Mathematics 131 (1992), 3-30.
MR 93m:03054.

47. Sharply transitive linear groups over algebraically closed fields,
with T. Grundhofer, A. Nesin, and H. Völklein,

Proceedings A.M.S. 111 (1991), 541-550. MR 91f:20002.

46. Homogeneous solvable groups,
with U. Felgner,

J. London Math. Soc 44 (1991), 102-120. MR 92m:20027.

45. Homogeneous tournaments revisited,

Geometriae Dedicatae 26 (1988), 231-240.

44. Orthogonal types in separably closed fields
with Z. Chatzidakis, S. Shelah, G. Srour, C. Wood,

in Classification Theory, J. Baldwin ed., Lecture Notes in Mathematics 1292 (1987), 72-88.

43. Homogeneous directed graphs I. The imprimitive case,

In Logic Colloquium 1985, Lolli et al. eds., 1987, 67-88.

Revised 2016

42. Stable finitely homogeneous structures,
with A. Lachlan,

Transactions American Mathematical Society 296 (1986), 815-850.

41. Some undecidable theories over p.a.c. fields,
with M. Jarden,

Annals of Pure and Applied Logic 30 (1986), 137-163.

40. ℵ₀-categorical, ℵ₀-stable structures,
with L. Harrington and A. Lachlan,

Annals of Pure and Applied Logic 28 (1985), 103-135.

39. On extensions of Presburger arithmetic,
with Francoise Point,

in Proceedings of the fourth Easter conference on model theory, (Groß Köris, 1986), 17-34,
Seminarberichte, 86, Humboldt University, Berlin, 1986.
03B25 (03C10 03F30) MR 87k:03002.

38. Decidable theories of pseudo-algebraically closed fields,

in Models and Sets, G. Müller and M. Richter eds., Lecture Notes in Mathematics 1103, Springer, NY, 1985, 83-101.

37. Aspects of ℵ₀-categorical theories,

In Proceedings of the Seventh ICLMPS, Salzburg, 1983, North-Holland, Amsterdam, 1986, 99-114.

36. Convexity properties and algebraic closure operators,
with H. Volger,

In Logic Colloquium 1983, Müller and Richter eds., Lecture Notes in Mathematics 1103 (1985), Springer, NY, 113-146.

35. Real closed rings II. Model theory,
with M. Dickmann,

Annals of Pure and Applied Logic 25 (1983), 213-231.

34. Real closed rings I. Residue rings of rings of continuous functions,
with M. Dickmann,

Fundamenta Mathematicae 126 (1986), 213-231.

33. Totally categorical theories,

in Proceedings of the ICM 1983, PWN, Warsaw, 1984, pp. 301-306.

32. Definability in power series rings of nonzero characteristic,

In Logic Colloquium 1983, G. Müller and M. Richter eds., Lecture Notes Math. 1103 (1985), 102-112.

31. Homogeneous finite groups,
with U. Felgner,

In Logic Colloquium 1980, D. van Dalen et al. eds., 1982, 69-81.

30. Undecidability of rational function fields in characteristic p,

In Logic Colloquium 1982, Lolli et al. eds., 1984, 85-95.

29. Decidability and undecidabilty theorems for p.a.c. fields,
with A. Macintyre and L. van den Dries,

Bulletin of the AMS 4 (1981), 101-104.

28. Note on a Nullstellensatz,
with Max Dickmann,

in Model theory and arithmetic (Paris, 1979-1980), pp. 111-114, Lecture Notes in Mathematics 890, Springer, Berlin-New York, 1981.
MR 83h:12032.

27. QE rings in characteristic pⁿ,
with C. Berline,

J. Symb. Logic 48 (1983), 140-162.

26. QE nilrings of prime characteristic,
with C. Berline,

Bull. Acad. Math. Belg. Ser. B 33 (1981), 3-17.

25. QE rings in characteristic p,
with C. Berline,

in Model Theory Year, M. Lerman et al. eds., Lecture Notes in Mathematics 859 (1980), 16-31. Springer, NY.

24. Rings of continuous functions: decision problems,

in Model Theory of Algebra and Arithmetic, L. Pacholski et al. eds.,
Lecture Notes in Mathematics 834 (1980), 44-92. Springer, NY.

23. Locally pure topological abelian groups: Elementary invariants,
with P. Schmitt,

Annals of Pure and Applied Logic 24 (1983), 49-85.

22. Undecidable L^t theories of topological abelian groups
with P. Schmitt,

J. Symb. Logic 46 (1981), 761-772.

21. Anneaux réels clos et anneaux de fonctions continues,
with M. Dickmann,

Contes Rendus Acad. Sciences 290 (1980), 1-4.

20. Superstable fields and groups,
with S. Shelah,

Annals of Mathematical Logic 18 (1980), 227-270.

19. Elimination des quantificateurs dans les faisceaux,
with M. Boffa,

Contes Rendus Acad. Sciences 290 (1980), 355-357.

18. Stable algebraic theories,

In Logic Colloquium 1978, Boffa et al. eds., 1979, 53-74.

17. ℵ₀-categorical nilrings II.

J. Symb. Logic 45 (1980), 291-301.

16. On ℵ₀-categorical nilrings,

Algebra Universalis 10 (1980), 27-30.

15. Superstable division rings,

In Logic Colloquium 1977, Macintyre et al. eds., 1978, 99-111.

14. Groups of small Morley rank,

Annals of Mathematical Logic 17 (1979), 1-28.

13. Totally categorical groups,
with W. Baur and A. Macintyre,

J. Algebra 57 (1979), 407-440.

12. On ℵ₀-categorical abelian-by-finite groups,
with J. Rosenstein,

J. Algebra 53 (1978), 188-226.

11. Amalgamation bases for commutative rings,

Israel J. Mathematics 25 (1976), 87-96.

10. Model Theoretic Algebra: Selected Topics,

Lecture Notes in Mathematics 521 (1975). Springer, NY.

9. Lindenbaum algebras and model companions,

Fundamenta Mathematicae 104(1979), 213-219.

8. Categoricity and stability of commutative rings,
with J. Reineke,

Annals of Mathematical Logic 10 (1976), 367-399.

7. Ideals in some nonstandard dedekind rings,

in Proceedings of the Louvain Model Theory Colloquium (1975),
P. Henrard ed., Editions Paul Castella, 1661 Albeuve, Switzerland, 1977, 28 pp.

6. Model theoretic algebra,

J. Symbolic Logic 41 (1976), 537-545.

5. Ideals of integers in nonstandard models of arithmetic,

in Model Theory and Algebra, Weispfenning and Saracino eds., Lecture Notes in Mathematics 498 (1975), pp. 60-90.

4. Second order forcing, existentially complete structures, and large cardinals

Fundamenta Mathematicae 87 (1975), 141-160.

3. Algebraically closed commutative rings,

J. Symbolic Logic 38 (1973), 493-499.

2. The model companion of a class of structures

J. Symbolic Logic 37 (1972), 546-556.

1. Ultrafilters and ultraproducts in nonstandard analysis,
with J. Hirschfeld,

In Contributions to Nonstandard Analysis, Luxemburg and Robinson, eds., North-Holland 1972, 261-279.

Seminar Proceedings

Universal graphs with forbidden subgraphs

Lecture Notes, Seminar on ordered algebraic structures, Paris, 2004/2005

Equipe de Logique Mathématique, Prépublications, 78. Delon, Dickmann, Gondard eds, Paris VII, February 2006.

This material is based in part upon work supported by the NSF under Grants No. DMS-9803417, DMS-0100794, and DMS-0600940. Any opinions, findings, conclusions, or recommendations expressed herein are those of the authors and do not necessarily reflect the views of the National Science Foundaion.