Stable Theories
T is called stable if it is κ-stable for some cardinal κ. Examples:
- The theory of any module over a ring is stable.
- The theory of a countable number of equivalence relations En for n a natural number such that each equivalence relation has an infinite number of equivalence classes and each equivalence class of En is the union of an infinite number of different classes of En+1 is stable but not superstable.
- Sela (2006) showed that free groups, and more generally torsion free hyperbolic groups, are stable. Free groups on more than one generator are not superstable.
- A differentially closed field is stable. If it has non-zero characteristic it is not superstable, and if it has zero characteristic it is totally transcendental.
Read more about this topic: Stable Theory
Famous quotes containing the words stable and/or theories:
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—D.H. (David Herbert)
“The two most far-reaching critical theories at the beginning of the latest phase of industrial society were those of Marx and Freud. Marx showed the moving powers and the conflicts in the social-historical process. Freud aimed at the critical uncovering of the inner conflicts. Both worked for the liberation of man, even though Marx’s concept was more comprehensive and less time-bound than Freud’s.”
—Erich Fromm (1900–1980)