Bulletin of Symbolic Logic 4 (1):17-36 (1998)
Abstract§1. Introduction. In this report we wish to describe recent work on a class of first order theories first introduced by Shelah in , the simple theories. Major progress was made in the first author's doctoral thesis . 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 . 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|.
Similar books and articles
A pragmatic modification of explicativity for the acceptance of hypotheses.I. J. Good & Alan F. McMichael - 1984 - Philosophy of Science 51 (1):120-127.
What is the problem of simplicity?Elliott Sober - 2002 - In Arnold Zellner, Hugo A. Keuzenkamp & Michael McAleer (eds.), Simplicity, Inference, and Modelling. Cambridge: Cambridge University Press. pp. 13-32.
The curve fitting problem: A solution.Peter Turney - 1990 - British Journal for the Philosophy of Science 41 (4):509-530.
Simplicity and Ontologies The trade-off between simplicity of theories and sophistication of ontologies.Aaron Sloman - unknown
Graceful Simplicity: Toward a Philosophy and Politics of Simple Living.Jerome M. Segal - 1999 - H. Holt & Co..
Added to PP
Historical graph of 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.
Divide and Conquer: Dividing Lines and Universality.Saharon Shelah - 2021 - Theoria 87 (2):259-348.
Supersimple ω-categorical groups and theories.David M. Evans & Frank O. Wagner - 2000 - Journal of Symbolic Logic 65 (2):767-776.
References found in this work
ℵ0-Categorical, ℵ0-stable structures.G. Cherlin, L. Harrington & A. H. Lachlan - 1985 - Annals of Pure and Applied Logic 28 (2):103-135.
Generic structures and simple theories.Z. Chatzidakis & A. Pillay - 1998 - Annals of Pure and Applied Logic 95 (1-3):71-92.
Hyperimaginaries and Automorphism Groups.D. Lascar & A. Pillay - 2001 - Journal of Symbolic Logic 66 (1):127-143.
An introduction to forking.Daniel Lascar & Bruno Poizat - 1979 - Journal of Symbolic Logic 44 (3):330-350.