Book Review
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Book Information:
Authors:
Gregory Cherlin and
Ehud Hrushovki
Title:
Finite structures with few types
Additional book information:
Annals of Math Studies, Princeton University Press,
Princeton, NJ,
2003,
vi + 193 pp.,
ISBN 0-691-11331-9,
$49.95$
Gisela Ahlbrandt and Martin Ziegler, Quasi-finitely axiomatizable totally categorical theories, Ann. Pure Appl. Logic 30 (1986), no. 1, 63–82. Stability in model theory (Trento, 1984). MR 831437, DOI 10.1016/0168-0072(86)90037-0
Peter J. Cameron, Oligomorphic permutation groups, London Mathematical Society Lecture Note Series, vol. 152, Cambridge University Press, Cambridge, 1990. MR 1066691, DOI 10.1017/CBO9780511549809
Gregory Cherlin, Large finite structures with few types, Algebraic model theory (Toronto, ON, 1996) NATO Adv. Sci. Inst. Ser. C: Math. Phys. Sci., vol. 496, Kluwer Acad. Publ., Dordrecht, 1997, pp. 53–105. MR 1481439
G. Cherlin, L. Harrington, and A. H. Lachlan, $\aleph _0$-categorical, $\aleph _0$-stable structures, Ann. Pure Appl. Logic 28 (1985), no. 2, 103–135. MR 779159, DOI 10.1016/0168-0072(85)90023-5
Ehud Hrushovski, Totally categorical structures, Trans. Amer. Math. Soc. 313 (1989), no. 1, 131–159. MR 943605, DOI 10.1090/S0002-9947-1989-0943605-1
W. M. Kantor, Martin W. Liebeck, and H. D. Macpherson, $\aleph _0$-categorical structures smoothly approximated by finite substructures, Proc. London Math. Soc. (3) 59 (1989), no. 3, 439–463. MR 1014866, DOI 10.1112/plms/s3-59.3.439
Byunghan Kim and Anand Pillay, Simple theories, Ann. Pure Appl. Logic 88 (1997), no. 2-3, 149–164. Joint AILA-KGS Model Theory Meeting (Florence, 1995). MR 1600895, DOI 10.1016/S0168-0072(97)00019-5
8. A.H. Lachlan.
Stable finitely homogeneous structures: a survey.
In Valeriote Hart, Lachlan, editor, Algebraic Model Theory, pages 145-161. Kluwer Academic Publisher, 1997.
Michael Morley, Categoricity in power, Trans. Amer. Math. Soc. 114 (1965), 514–538. MR 175782, DOI 10.1090/S0002-9947-1965-0175782-0
Rohit Parikh, An $\aleph _{0}$-categorical theory whose language is countably infinite, Proc. Amer. Math. Soc. 49 (1975), 216–218. MR 381979, DOI 10.1090/S0002-9939-1975-0381979-9
Joseph G. Rosenstein, Theories which are not $\aleph _{0}$-categorical, Proceedings of the Summer School in Logic (Leeds, 1967) Springer, Berlin, 1968, pp. 273–278. MR 0237310
Boris Zilber, Uncountably categorical theories, Translations of Mathematical Monographs, vol. 117, American Mathematical Society, Providence, RI, 1993. Translated from the Russian by D. Louvish. MR 1206477, DOI 10.1090/mmono/117
- 1.
- G. Ahlbrandt and M. Ziegler.
Quasi-finitely axiomatizable totally categorical theories.
Annals of Pure and Applied Logic, 30:63-82, 1986. MR 0831437
- 2.
- P. Cameron.
Oligomorphic Permutation Groups.
Number 152 in London Math. Society Lecture Note Series. Cambridge University Press, 1990. MR 1066691
- 3.
- G.L. Cherlin.
Large finite structures with few types.
In Valeriote Hart, Lachlan, editor, Algebraic Model Theory, pages 53-107. Kluwer Academic Publisher, 1997. MR 1481439
- 4.
- G.L. Cherlin, L. Harrington, and A.H. Lachlan.
-categorical, 
-stable structures.
Annals of Pure and Applied Logic, 28:103-135, 1985. MR 0779159
- 5.
- E. Hrushovski.
Totally categorical structures.
Transactions of the American Mathematical Society, 313:131-159, 1989. MR 0943605
- 6.
- W. Kantor, M. Liebeck, and H.D. Macpherson.
-categorical structures smoothly approximable by finite substructures.
Proceedings London Math. Soc., 59:439-463, 1989. MR 1014866
- 7.
- B. Kim and A. Pillay.
Simple theories.
Annals of Pure and Applied Logic, 88:149-164, 1997. MR 1600895
- 8.
- A.H. Lachlan.
Stable finitely homogeneous structures: a survey.
In Valeriote Hart, Lachlan, editor, Algebraic Model Theory, pages 145-161. Kluwer Academic Publisher, 1997.
- 9.
- M. Morley.
Categoricity in power.
Transactions of the American Mathematical Society, 114:514-538, 1965. MR 0175782
- 10.
- Rohit Parikh.
An 
-categorical theory whose language is countably infinite.
Proc. Amer. Math. Soc., 49:216-218, 1975. MR 0381979
- 11.
- J. Rosenstein.
Theories which are not 
-categorical.
In M.H. Löb, editor, Proceedings of the Summer School in Logic (Leeds, 1967). Springer-Verlag, 1968,
LNM 70. MR 0237310
- 12.
- B.I. Zil'ber.
Uncountably Categorical Theories.
Translations of the American Mathematical Society, 117. American Mathematical Society, 1993,
summary of earlier work. MR 1206477
Review Information:
Reviewer:
John T. Baldwin
Affiliation:
University of Illinois at Chicago
Email:
jbaldwin@uic.edu
Journal:
Bull. Amer. Math. Soc.
41 (2004), 391-394
Published electronically:
March 4, 2004
Review copyright:
© Copyright 2004
American Mathematical Society
