From stability to simplicity

Bulletin of Symbolic Logic 4 (1):17-36 (1998)
  Copy   BIBTEX


§1. Introduction. In this report we wish to describe recent work on a class of first order theories first introduced by Shelah in [32], the simple theories. Major progress was made in the first author's doctoral thesis [17]. We will give a survey of this, as well as further works by the authors and others.The class of simple theories includes stable theories, but also many more, such as the theory of the random graph. Moreover, many of the theories of particular algebraic structures which have been studied recently turn out to be simple. The interest is basically that a large amount of the machinery of stability theory, invented by Shelah, is valid in the broader class of simple theories. Stable theories will be defined formally in the next section. An exhaustive study of them is carried out in [33]. Without trying to read Shelah's mind, we feel comfortable in saying that the importance of stability for Shelah lay partly in the fact that an unstable theory T has 2λ many models in any cardinal λ ≥ ω1 + |T|.



    Upload a copy of this work     Papers currently archived: 92,931

External links

Setup an account with your affiliations in order to access resources via your University's proxy server

Through your library

Similar books and articles


Added to PP

38 (#431,997)

6 months
12 (#243,608)

Historical graph of downloads
How can I increase my downloads?

Citations of this work

Pseudofinite structures and simplicity.Darío García, Dugald Macpherson & Charles Steinhorn - 2015 - Journal of Mathematical Logic 15 (1):1550002.
The number of types in simple theories.Enrique Casanovas - 1999 - Annals of Pure and Applied Logic 98 (1-3):69-86.
Simplicity, and stability in there.Byunghan Kim - 2001 - Journal of Symbolic Logic 66 (2):822-836.
Supersimple ω-categorical groups and theories.David M. Evans & Frank O. Wagner - 2000 - Journal of Symbolic Logic 65 (2):767-776.

View all 11 citations / Add more citations

References found in this work

Generic structures and simple theories.Z. Chatzidakis & A. Pillay - 1998 - Annals of Pure and Applied Logic 95 (1-3):71-92.
ℵ0-Categorical, ℵ0-stable structures.G. Cherlin, L. Harrington & A. H. Lachlan - 1985 - Annals of Pure and Applied Logic 28 (2):103-135.
Laforte, G., see Downey, R.T. Arai, Z. Chatzidakis & A. Pillay - 1998 - Annals of Pure and Applied Logic 95 (1-3):287.
An introduction to forking.Daniel Lascar & Bruno Poizat - 1979 - Journal of Symbolic Logic 44 (3):330-350.
[Omnibus Review].Anand Pillay - 1984 - Journal of Symbolic Logic 49 (1):317-321.

View all 20 references / Add more references