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

**1.**G. Ahlbrandt and M. Ziegler.

Quasi-finitely axiomatizable totally categorical theories.*Annals of Pure and Applied Logic*, 30:63-82, 1986. MR**87k:03026****2.**P. Cameron.*Oligomorphic Permutation Groups*.

Number 152 in London Math. Society Lecture Note Series. Cambridge University Press, 1990. MR**92f:20002****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**99d:03031****4.**G.L. Cherlin, L. Harrington, and A.H. Lachlan.

-categorical, -stable structures.*Annals of Pure and Applied Logic*, 28:103-135, 1985. MR**86g:03054****5.**E. Hrushovski.

Totally categorical structures.*Transactions of the American Mathematical Society*, 313:131-159, 1989. MR**90f:03064****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**91e:03033****7.**B. Kim and A. Pillay.

Simple theories.*Annals of Pure and Applied Logic*, 88:149-164, 1997. MR**99b:03049****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**31:58****10.**Rohit Parikh.

An -categorical theory whose language is countably infinite.*Proc. Amer. Math. Soc.*, 49:216-218, 1975. MR**52:2868****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**38:5600****12.**B.I. Zil'ber.*Uncountably Categorical Theories*.

Translations of the American Mathematical Society, 117. American Mathematical Society, 1993,

summary of earlier work. MR**94h:03059**

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

MSC (2000): Primary 03C45; Secondary 20B99

Published electronically: March 4, 2004

Review copyright: © Copyright 2004 American Mathematical Society