HOME | BESTSELLERS | NEW RELEASES | PRICE WATCH | FICTION | BIOGRAPHIES | E-BOOKS |
+ PRICE WATCH
* Amazon pricing is not included in price watch
Finite Structures with Few Types. (AM-152) (Annals of Mathematics Studies) 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.Read More
from£16.95 | RRP: * Excludes Voucher Code Discount Also available Used from £26.00
- 0691113327
- 9780691113326
- Gregory Cherlin, Ehud Hrushovski
- 23 December 2002
- Princeton University Press
- Paperback (Book)
- 200
As an Amazon Associate we earn from qualifying purchases. If you click through any of the links below and make a purchase we may earn a small commission (at no extra cost to you). Click here to learn more.
Would you like your name to appear with the review?
We will post your book review within a day or so as long as it meets our guidelines and terms and conditions. All reviews submitted become the licensed property of www.find-book.co.uk as written in our terms and conditions. None of your personal details will be passed on to any other third party.
All form fields are required.