Titlebook: Simple Theories; Frank O. Wagner Book 2000 Springer Science+Business Media B.V. 2000 Algebraic structure.Equivalence.algebra.model theory.

dilate

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不能平静

Preliminaries,el Morley’s study of uncountably categorical theories, where he defined .-stability, and for some time remained in the categorical context. This changed when Saharon Shelah embarked on an ambitious programme of classifying the models of a complete first-order theory, using his newly invented notion

残酷的地方

发怨言

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disciplined

Groups, general structural considerations in a context where . no group was given. Moreover, they are amenable to a more detailed model-theoretic study: due to the homogeneity imposed by the group law, a group in a simple theory often has a more friendly behaviour than a general simple structure.

CHART

Supersimple Theories,supersimplicity stems from the fact that it allows a global, ordinal-valued rank, invariant under definable bijections, which orders definable sets and types and is compatible with independence. In fact, there are two (main) ranks; one suitable for complete types and one suitable for partial types.

Gleason-score

flaunt

Simplicity,s than . and be a subset of C, and every tuple will have length less than . and come from C. Since every model of . of cardinality less than . can be elementarily embedded into C, this is no restriction, but it simplifies the arguments and helps the intuition, as everything takes place inside a fixed “universal domain”.

HAVOC

maintenance

Preliminaries, tried in [149, 152] to extend the framework, defining a well-behaved class of unstable first-order theories which he called “simple unstable”. However, symmetry of forking for those theories eluded him, and at the time those papers did not receive the attention they deserved.