UID:
almafu_9958094790702883
Format:
1 online resource (741 p.)
Edition:
Rev. ed.
ISBN:
1-281-71606-5
,
9786611716066
,
0-08-088024-X
Series Statement:
Studies in logic and the foundations of mathematics ; v. 92
Content:
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 m
Note:
Description based upon print version of record.
,
Front Cover; Classification Theory and the Number of Non-Isomorphic Models; Copyright Page; Contents; Acknowledgements; Introduction; Introduction to the revised edition; Open problems; Added in proof; Notation; Chapter I. Preliminaries; 0. Introduction; 1. Preliminaries and saturation; 2. Order, stability and indiscernibles; Chapter II. Ranks and Incomplete Types; 0. Introduction; 1. Ranks of types; 2. Stability, ranks and definability; 3. Ranks, degrees and superstability; 4. The f.c.p., the independence property and the strict order property; Chapter III. Global Theory; 0. Introduction
,
1. Forking2. The finite equivalence relation theorem; 3. The instability spectrum; 4. Further properties of forking; 5. The fist stability cardinal; 6. Imaginary elements; 7. Instability; Chapter IV. Prime Models; 0. Introduction; 1. The set of axioms; 2. Examples of F's; 3. General properties of F-primary models; 4. Prime models for stable theories; 5. Various results; Chapter V. More on Types and Saturated Models; 0. Introduction; 1. Orthogonality, regularity and minimality of types; 2. Dimensions and orders between indiscernible sets; 3. Weighted dimensions and superstability
,
4. Semi-regular and semi-minimal types5. Multi-dimensional theories; 6. Cardinality-quantifiers and two-cardinal theorems; 7. Ranks revisited; Chapter VI. Saturation of Ultraproducts; 0. Introduction; 1. Reduced products and regular filters; 2. Good filters and compactness of reduced products; 3. Constructing ultrafilters; 4. Keisler's order; 5. Saturation of ultrapowers and categoricity of pseudoelementary classes; 6. Saturation of ultralimits; Chapter VII. Construction of Models; 0. Introduction; 1. Skolem functions and generalizations of saturativity
,
2. Generalized Ehrenfeucht-Mostowski models3. On the f.c.p., uniform trees and |D(T)| 〉 |T| = Xo; 4. Semi-definability; 5. Hanf numbers of omitting types; Chapter VIII. The Number of Non-Isomorphic Models in Pseudo-Elementary; 0. Introduction; 1. Independence of types; 2. Unsupmtable theories; 3. Saturated models and the case λ = |T1|; 4. Categoricity, saturation and homogeneity up to a cardinality; Chapter IX. Categoricity and the Number of Models in Elementary Classes; 0. Introduction; 1. Supratable theories and categoricity; 2. On the lower parts of the spectrum
,
Chapter X. Classification for Faxo-Saturated Models0. Introduction; 1. Preliminaries; 2. The dimensional order property; 3. The decomposition lemma; 4. Deepness; 5. Deep theories have many non-isomorphic models; 6. Infinite depth; 7. Trivial types; Chapter XI. The Decomposition Theorem; 0. Introduction; 1. Stationarization; 2. The axiomatic treatment; 3. Specifying the axiomatic treatment; Chapter XII. The Main Gap for Countable Theories; 0. Introduction; 1. On Fkλ and Ffλ; 2. Stable systems; 3. On good sets; 4. The otop/existence dichotomy
,
5. From the (X0, 2)-existence property to the (λ, 2)-existence property
,
English
Additional Edition:
ISBN 0-444-70260-1
Language:
English
Bookmarklink
