Abstract
Mathematics often proceeds from the specific to the general, and the development of simplicity theory is no exception to the rule. It began with Michael Morley’s study of uncountably categorical theories, where he defined ω-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 of “forking” and Rowbottom’s “stability”. Unstable theories have the maximal number of models and are thus considered unclassifiable; nevertheless, he 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.
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Wagner, F.O. (2000). Preliminaries. In: Simple Theories. Mathematics and Its Applications, vol 503. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-3002-0_1
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