Introduction Though our focus is extending classification theory in various directions, there is here material which, I think, will interest researchers in quite different directions: general topology, Boolean algebras, set theory ...
Proceedings of the U.S.-Israel Workshop on Model Theory in Mathematical Logic Held in Chicago, Dec. 15-19, 1985 John T. Baldwin ... 1149; Universal Algebra and Lattice Theory. ... 1182, S. Shelah, Around Classification Theory of Models.
Classification theory and the number of non-isomorphic models/S. Shelah. —– 2nd ed. p. cm. –— (Studies in logic and the foundations of mathematics; v. 92) Includes bibliographical references. ISBN 0–444–70260–1 1. Model theory.
Author: S. Shelah
In this research monograph, the author's work on classification and related topics are presented. This revised edition brings the book up to date with the addition of four new chapters as well as various corrections to the 1978 text. The additional chapters X - XIII present the solution to countable first order T of what the author sees as the main test of the theory. In Chapter X the Dimensional Order Property is introduced and it is shown to be a meaningful dividing line for superstable theories. In Chapter XI there is a proof of the decomposition theorems. Chapter XII is the crux of the matter: there is proof that the negation of the assumption used in Chapter XI implies that in models of T a relation can be defined which orders a large subset of m|M|. This theorem is also the subject of Chapter XIII.
There is a long tradition in studying connections between Borel structure of Polish spaces (descriptive set theory) and model theory. The connection arises from the fact that any class of countable structures can be coded into a subset ...
Author: Sy-David Friedman
Publisher: American Mathematical Soc.
Descriptive set theory is mainly concerned with studying subsets of the space of all countable binary sequences. In this paper the authors study the generalization where countable is replaced by uncountable. They explore properties of generalized Baire and Cantor spaces, equivalence relations and their Borel reducibility. The study shows that the descriptive set theory looks very different in this generalized setting compared to the classical, countable case. They also draw the connection between the stability theoretic complexity of first-order theories and the descriptive set theoretic complexity of their isomorphism relations. The authors' results suggest that Borel reducibility on uncountable structures is a model theoretically natural way to compare the complexity of isomorphism relations.
In Around classification theory of models , volume 1182 of Lecture Notes in Mathematics , pages 47 - 90. Springer , Berlin , 1986 . Saharon Shelah , Classifying generalized quantifiers . In Around classification theory of models ...
(1978) Toward model theory through recursive saturation, J. Symb. Logic 43, 183– 206. JüRG SCHMIT and JüRGEN SCHMIDT (1987) Enlargements without urelements, Colloq. Math. 52, 1–22. S. SHELAH (1978) Classification Theory and the Number ...
Author: C.C. Chang
Since the second edition of this book (1977), Model Theory has changed radically, and is now concerned with fields such as classification (or stability) theory, nonstandard analysis, model-theoretic algebra, recursive model theory, abstract model theory, and model theories for a host of nonfirst order logics. Model theoretic methods have also had a major impact on set theory, recursion theory, and proof theory. This new edition has been updated to take account of these changes, while preserving its usefulness as a first textbook in model theory. Whole new sections have been added, as well as new exercises and references. A number of updates, improvements and corrections have been made to the main text.
Recently classification theory and the theory of minimal models of algebraic varieties has made remarkable progress (cf. [KMM], [Mor5]), where the study of certain singularities (terminal, canonical, log—terminal etc.) ...
Author: Takao Fujita
Publisher: Cambridge University Press
A polarised variety is a modern generalization of the notion of a variety in classical algebraic geometry. It consists of a pair: the algebraic variety itself, together with an ample line bundle on it. Using techniques from abstract algebraic geometry that have been developed over recent decades, Professor Fujita develops classification theories of such pairs using invariants that are polarised higher-dimensional versions of the genus of algebraic curves. The heart of the book is the theory of D-genus and sectional genus developed by the author, but numerous related topics are discussed or surveyed. Proofs are given in full in the central part of the development, but background and technical results are sometimes just sketched when the details are not essential for understanding the key ideas. Readers are assumed to have some background in algebraic geometry, including sheaf cohomology, and for them this work will provide an illustration of the power of modern abstract techniques applied to concrete geometric problems. Thus the book helps the reader not only to understand about classical objects but also modern methods, and so it will be useful not only for experts but also non-specialists and graduate students.