dilate 发表于 2025-3-21 18:12:00

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不能平静 发表于 2025-3-21 21:50:09

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 发表于 2025-3-22 04:27:00

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发怨言 发表于 2025-3-22 06:56:03

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disciplined 发表于 2025-3-22 08:59:00

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 发表于 2025-3-22 16:29:01

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 发表于 2025-3-22 19:10:13

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flaunt 发表于 2025-3-22 21:16:35

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 发表于 2025-3-23 01:50:44

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maintenance 发表于 2025-3-23 05:53:35

Preliminaries, tried in 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.
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查看完整版本: Titlebook: Simple Theories; Frank O. Wagner Book 2000 Springer Science+Business Media B.V. 2000 Algebraic structure.Equivalence.algebra.model theory.