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In model theory, a complete theory is called stable if it does not have too many types. One goal of classification theory is to divide all complete theories into those whose models can be classified and those whose models are too complicated to classify, and to classify all models in the cases where this can be done. Roughly speaking, if a theory is not stable then its models are too complicated and numerous to classify, while if a theory is stable there might be some hope of classifying its models, especially if the theory is superstable or totally transcendental. Stability theory was started by , who introduced several of the fundamental concepts, such as totally transcendental theories and the Morley rank. Stable and superstable theories were first introduced by , who is responsible for much of the development of stability theory. The definitive reference for stability theory is , though it is notoriously hard even for experts to read. ==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 κ-stable for any infinite cardinal κ. *''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. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Stable theory」の詳細全文を読む スポンサード リンク
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