About: Stable theory

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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.

Attributes	Values
rdfs:label	Stable theory (en)
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. (en)
dcterms:subject	Model theory
Wikipage page ID	15828771 (xsd:integer)
Wikipage revision ID	1055755970 (xsd:integer)
Link from a Wikipage to another Wikipage	Cambridge University Press List of first-order theories Model (logic) Model theory Module (mathematics) Morley rank Hyperbolic group Peano arithmetic Integral domain Presburger arithmetic Saharon Shelah Continuum hypothesis Angus Macintyre Complete theory Half graph Spectrum of a theory Total order Divisibility (ring theory) Divisible group Heisenberg group Linear algebraic group Morley's categoricity theorem Stability spectrum Field (mathematics) Nilpotent group Differentially closed field Direct sum Graduate Texts in Mathematics Israel Journal of Mathematics Ring (mathematics) Abelian group Model theory Torsion-free group Torsion group Boolean algebra (structure) Free group Algebraically closed Ordered set Cancellative semigroup Categorical theory Real closed field Type (model theory) Springer-Verlag Characteristic of a field Group of finite Morley rank Complete type Cardinal (mathematics)
Link from a Wikipage to an external page	https://archive.org/details/modeltheory0000hodg https://archive.org/details/classificationth0092shel http://www.math.uiuc.edu/People/pillay/lecturenotes.applied.pdf http://www.math.uiuc.edu/People/pillay/lecturenotes.stability.pdf https://web.archive.org/web/20081217001510/http:/www.math.uiuc.edu/People/pillay/lecturenotes_modeltheory.pdf
sameAs	Stable theory Stable theory Stable theory
dbp:wikiPageUsesTemplate	dbt:Springer dbt:Citation dbt:For dbt:Harv dbt:Harvtxt
first	J. T. (en) M.A. (en) E.A. (en)
id	S/s087100 (en) s/s087080 (en)
last	Baldwin (en) Palyutin (en) Taitslin (en)
title	Stability theory (en) Stable and unstable theories (en)
has 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 . (en)
prov:wasDerivedFrom	wikipedia-en:Stable_theory?oldid=1055755970&ns=0
page length (characters) of wiki page	14595 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Stable_theory
is Link from a Wikipage to another Wikipage of	List of first-order theories Model theory NIP (model theory) Totally transcendental Totally transcendental theory Interpretation (model theory) List of mathematical logic topics Maryanthe Malliaris Timeline of mathematical logic Ehud Hrushovski Theory Stable group Half graph Stability Classification theory True arithmetic Stability spectrum Differentially closed field Forking extension Rami Grossberg Abstract elementary class

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