Classification Theory and the Number of Non-Isomorphic Models

Saharon Shelah9780444702609, 0444702601, 9780080880242

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.