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:
“You mustn’t look in my novel for the old stable ego of the character. There is another ego, according to whose action the individual is unrecognisable.”
—D.H. (David Herbert)
“In the course of a life devoted less to living than to reading, I have verified many times that literary intentions and theories are nothing more than stimuli and that the final work usually ignores or even contradicts them.”
—Jorge Luis Borges (1899–1986)