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
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