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Statements

Subject Item
dbr:Stable_theory
rdfs:label
Stable theory
rdfs:comment
In the mathematical field of 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.
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dbc:Model_theory
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15828771
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1055755970
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n11:classificationth0092shel n13:lecturenotes.applied.pdf n13:lecturenotes.stability.pdf n14:lecturenotes_modeltheory.pdf n11:modeltheory0000hodg
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dbp:first
E.A. J. T. M.A.
dbp:id
S/s087100 s/s087080
dbp:last
Baldwin Taitslin Palyutin
dbp:title
Stable and unstable theories Stability theory
dbo:abstract
In the mathematical field of 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, as mentioned, e.g., in .
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wikipedia-en:Stable_theory?oldid=1055755970&ns=0
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wikipedia-en:Stable_theory