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.
General
Is the information for this product incomplete, wrong or inappropriate?
Let us know about it.
Does this product have an incorrect or missing image?
Send us a new image.
Is this product missing categories?
Add more categories.
Review This Product
No reviews yet - be the first to create one!
Welcome to Loot.co.za!
Sign in / Register |Wishlists & Gift Vouchers |Help | Advanced search
