Definitions
T will be a complete theory in some language.
- T is called κ-stable (for an infinite cardinal κ) if for every set A of cardinality κ the set of complete types over A has cardinality κ.
- ω-stable is an alternative name for ℵ0-stable.
- T is called stable if it is κ-stable for some infinite cardinal κ
- T is called unstable if it is not k-stable for any infinite cardinal k.
- T is called superstable if it is κ-stable for all sufficiently large cardinals κ.
- Totally transcendental theories are those such that every formula has Morley rank less than ∞.
As usual, a model of some language is said to have one of these properties if the complete theory of the model has that property.
An incomplete theory is defined to have one of these properties if every completion, or equivalently every model, has this property.
Read more about this topic: Stable Theory
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