Series: Lecture Notes in Logic (No. 29)
Hardback (ISBN-13: 9780521884242)
Page extent: 224 pages
Size: 228 x 152 mm
The Annual European Meeting of the Association for Symbolic Logic, generally known as the Logic Colloquium, is the most prestigious annual meeting in the field. Many of the papers presented there are invited surveys of recent developments, and the rest of the papers are chosen to complement the invited talks. This volume includes surveys, tutorials, and selected research papers from the 2004 meeting. Highlights include a tutorial survey of the recent highpoints of universal algebra, written by a leading expert; explorations of foundational questions; and a quartet of model theory papers giving an excellent reflection of current work in model theory, from the most abstract aspect ‘abstract elementary classes’ to issues around p-adic integration.
* Contain contributions from leading experts in key areas of logic, including
set theory, model theory, universal algebra, recursion theory, and philosophy
of mathematics
Contents
0. Introduction; 1. Abstract elementary classes: some answers, more questions John T. Baldwin; 2. On the density of Hausdorff ultrafilters Tomek Bartoszynski and Saharon Shelah; 3. Zero groups and maximal tori Alessandro Berarducci; 4. Constructive set theory with operations A. Cantini and L. Crosilla; 5. Parametrized local zeta functions Raf Cluckers; 6. Colourings of hypergraphs, permutation groups and CSP's Benoit Larose and Lucien Haddad; 7. Congruence, tolerance identities; congruence modularity; shifting principle Paolo Lipparini; 8. Universes in type theory part I - inaccessibles and Mahlo Anton Setzer; 9. Hausdorff dimension and weak truth table reducibility Frank Stephan; 10. Computation and the explanation of intelligent behaviours: ethnologically motivated restart Guglielmo Tamburrini and Edoardo Datteri; 11. Constructible sheaves and definability Ivan Tomasic; 12. An overview of modern universal algebra Ross Willard.
Series: New Mathematical Monographs (No. 6)
Hardback (ISBN-13: 9780521878579)
40 worked examples
Page extent: 432 pages
Size: 228 x 152 mm
Detailing the main methods in the theory of involutive systems of complex vector fields this book examines the major results from the last twenty five years in the subject. One of the key tools of the subject - the Baouendi-Treves approximation theorem - is proved for many function spaces. This in turn is applied to questions in partial differential equations and several complex variables. Many basic problems such as regularity, unique continuation and boundary behaviour of the solutions are explored. The local solvability of systems of partial differential equations is studied in some detail. The book provides a solid background for others new to the field and also contains a treatment of many recent results which will be of interest to researchers in the subject.
* Details the main tools and methods in the theory of involutive systems
of complex vector fields * The Baouendi-Treves approximation theorem is
proved for many function spaces * Provides a solid background for beginners
in the field and also contains a treatment of many recent results of interest
to researchers in the subject
Contents
Preface; 1. Locally integrable structures; 2. The Baouendi-Treves approximation formula; 3. Sussmann’s orbits and unique continuation; 4. Local solvability of vector fields; 5. The FBI transform and some applications; 6. Some boundary properties of solutions; 7. The differential complex associated to a formally integrable structure; 8. Local solvability in locally integrable structures; Epilogue; Bibliography; A. Hardy space lemmas.
Series: Lecture Notes in Logic (No. 30)
Hardback (ISBN-13: 9780521889810)
Page extent: 200 pages
Size: 228 x 152 mm
This book addresses a gap in the model-theoretic understanding of valued fields that has, until now, limited the interactions of model theory with geometry. It contains significant developments in both pure and applied model theory. Part I of the book is a study of stably dominated types. These form a subset of the type space of a theory that behaves in many ways like the space of types in a stable theory. This part begins with an introduction to the key ideas of stability theory for stably dominated types. Part II continues with an outline of some classical results in the model theory of valued fields and explores the application of stable domination to algebraically closed valued fields. The research presented here is made accessible to the general model theorist by the inclusion of the introductory sections of each part.
* Background sections on stability theory and valued fields * Comprehensive
explication of new ideas which have been previously discussed but not published
Contents
1. Introduction; Part I. Stable Domination: 2. Some background on stability theory; 3. Definition and basic properties of Stc; 4. Invariant types and change of base; 5. A combinatorial lemma; 6. Strong codes for germs; Part II. Independence in ACVF: 7. Some background on algebraically closed valued fields; 8. Sequential independence; 9. Growth of the stable part; 10. Types orthogonal to Γ; 11. Opacity and prime resolutions; 12. Maximally complete fields and domination; 13. Invariant types; 14. A maximum modulus principle; 15. Canonical bases and independence given by modules; 16. Other Henselian fields.