Book Search Options:  

 

 
Google full text of our books:

     
bookjacket

Finite Structures with Few Types. (AM-152)
Gregory Cherlin & Ehud Hrushovski

Paperback | 2003 | $69.00 | £47.95 | ISBN: 9780691113326
200 pp. | 6 x 9
Add to Shopping Cart


Chapter 1[PDF] pdf-icon

Google full text of this book:
 

This book applies model theoretic methods to the study of certain finite permutation groups, the automorphism groups of structures for a fixed finite language with a bounded number of orbits on 4-tuples. Primitive permutation groups of this type have been classified by Kantor, Liebeck, and Macpherson, using the classification of the finite simple groups.

Building on this work, Gregory Cherlin and Ehud Hrushovski here treat the general case by developing analogs of the model theoretic methods of geometric stability theory. The work lies at the juncture of permutation group theory, model theory, classical geometries, and combinatorics.

The principal results are finite theorems, an associated analysis of computational issues, and an "intrinsic" characterization of the permutation groups (or finite structures) under consideration. The main finiteness theorem shows that the structures under consideration fall naturally into finitely many families, with each family parametrized by finitely many numerical invariants (dimensions of associated coordinating geometries).

The authors provide a case study in the extension of methods of stable model theory to a nonstable context, related to work on Shelah's "simple theories." They also generalize Lachlan's results on stable homogeneous structures for finite relational languages, solving problems of effectivity left open by that case. Their methods involve the analysis of groups interpretable in these structures, an analog of Zilber's envelopes, and the combinatorics of the underlying geometries. Taking geometric stability theory into new territory, this book is for mathematicians interested in model theory and group theory.

Series:

Subject Area:

VISIT OUR MATH WEBSITE

For hardcover/paperback orders in United States, Canada, Latin America, Asia, and Australia

 Paperback : $69.00 ISBN: 9780691113326

Add to shopping cart
View contents of your shopping cart

For hardcover/paperback orders in Europe, Africa, the Middle East, India, and Pakistan

 Paperback : $47.95 ISBN: 9780691113326

Add to shopping cart
View contents of your shopping cart

Prices subject to change without notice

File created: 8/8/2015

Questions and comments to: webmaster@press.princeton.edu
Princeton University Press

New Book E-mails
New In Print
PUP Blog
Videos/Audios
Princeton APPS
Sample Chapters
Subjects
Series
Catalogs
Princeton Legacy Library
Exam/Desk Copy
Textbooks
Media/Reviewers
Rights/Permissions
Ordering
Recent Awards
Princeton Shorts
Freshman Reading
PUP Europe
About Us
Contact Us
Links
F.A.Q.
MATH SITE
PUP Home


Bookmark and Share
Send me emails
about new books in:
Mathematics
More Choices