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Book Information

Author(s): 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, $49.95, 0-691-11331-9

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Quasi-finitely axiomatizable totally categorical theories.
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Oligomorphic Permutation Groups.
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3.: G.L. Cherlin.
Large finite structures with few types.
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4.: G.L. Cherlin, L. Harrington, and A.H. Lachlan.
$\aleph_0$ -categorical, $\aleph_0$ -stable structures.
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Totally categorical structures.
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$\aleph_0$ -categorical structures smoothly approximable by finite substructures.
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Simple theories.
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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 $\aleph \sb{0}$ -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 $\aleph_0$ -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.
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summary of earlier work. MR 94h:03059

Reviewer(s):
John T. Baldwin
Affiliation: University of Illinois at Chicago
Email: jbaldwin@uic.edu

MSC (2000): Primary 03C45; Secondary 20B99
DOI: 10.1090/S0273-0979-04-01014-6
PII: S 0273-0979(04)01014-6
Posted: March 4, 2004
Copyright of article: Copyright 2004, American Mathematical Society

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ISSN 1088-9485(e) ISSN 0273-0979(p)

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