A survey of basic stability theory, with particular emphasis on orthogonality and regular types

A selfcontained exposition is given of a part of stability theory in model theory, the part that deals with the concepts of orthogonality, weight and regularity. The necessary background from earlier parts of stability theory is explained but proofs in this part are given in outline only or not at all.

[1]  M. Morley Categoricity in power , 1965 .

[2]  Chen C. Chang,et al.  Model Theory: Third Edition (Dover Books On Mathematics) By C.C. Chang;H. Jerome Keisler;Mathematics , 1966 .

[3]  Remark to “local definability theory” of Reyes☆ , 1971 .

[4]  Gerald E. Sacks,et al.  Saturated Model Theory , 1972 .

[5]  Saharon Shelah,et al.  Uniqueness and characterization of prime models over sets for totally transcendental first-order theories , 1972, Journal of Symbolic Logic.

[6]  Daniel Lascar,et al.  Ranks and definability in superstable theories , 1976 .

[7]  M. Makkai,et al.  First order categorical logic , 1977 .

[8]  Saharon Shelah Hanf Number of Omitting Type for Simple First-Order Theories , 1979, J. Symb. Log..

[9]  Saharon Shelah,et al.  On uniqueness of prime models , 1979, Journal of Symbolic Logic.

[10]  Bruno Poizat,et al.  An Introduction to Forking , 1979, J. Symb. Log..

[11]  Daniel Lascar,et al.  Ordre de Rudin-Keisler et Poids Dans les Theories Stables , 1982, Math. Log. Q..

[12]  S. Shelah The spectrum problem II: Totally transcendental and infinite depth , 1982 .

[13]  S. Shelah The spectrum problem I: ℵɛ-satuarted models, the main gap , 1982 .

[14]  Saharon Shelah,et al.  Classification theory for non-elementary classes I: The number of uncountable models of $$\psi \in L_{w_1 ,w} $$ . Part B. Part B , 1983 .

[15]  Elisabeth Bouscaren Countable Models of Multidimensional 0-Stable Theories , 1983, J. Symb. Log..

[16]  Saharon Shelah,et al.  Classification theory for non-elementary classes I: The number of uncountable models ofψ ∈Lω_1, ω. Part A , 1983 .

[17]  Saharon Shelah,et al.  A proof of vaught’s conjecture forω-stable theories , 1984 .

[18]  Victor Harnik,et al.  Fundamentals of forking , 1984, Ann. Pure Appl. Log..

[19]  Leo Harrington,et al.  An exposition of Shelah's "main gap": counting uncountable models of ω-stable and superstable theories , 1985, Notre Dame J. Formal Log..