Fundamentals of stability theory. (English) Zbl 0685.03024

Perspectives in Mathematical Logic. Berlin etc.: Springer-Verlag. XIII, 447 p.; DM 128.00 (1988).
John Baldwin’s book is the latest of a number of books on the subject of stability theory. It is also the most exhaustive, with the probable exception of the expected revised edition of Shelah. The following goals are attained: the structure/non-structure theorem for the class K of suitably saturated models of a superstable theory, and proofs of the Vaught and Morley conjectures for \(\omega\)-stable theories. (All these results are due to Shelah). All the prerequisites for these results appear, namely forking, prime models, regular types and orthogonality. There are also sections on additional topics such as stable groups, and normalisation. The author has a marked preference for the axiomatic approach, namely finding the most general and common context for proving results. The book also contains a pretty complete bibliography on the subject.
Reviewer: A.Pillay


03C45 Classification theory, stability, and related concepts in model theory
03-02 Research exposition (monographs, survey articles) pertaining to mathematical logic and foundations