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- W4298086144 abstract "Non-forking is one of the most important notions in modern model theory capturing the idea of a generic extension of a type (which is a far-reaching generalization of the concept of a generic point of a variety). To a countable first-order theory we associate its non-forking spectrum - a function of two cardinals kappa and lambda giving the supremum of the possible number of types over a model of size lambda that do not fork over a sub-model of size kappa. This is a natural generalization of the stability function of a theory. We make progress towards classifying the non-forking spectra. On the one hand, we show that the possible values a non-forking spectrum may take are quite limited. On the other hand, we develop a general technique for constructing theories with a prescribed non-forking spectrum, thus giving a number of examples. In particular, we answer negatively a question of Adler whether NIP is equivalent to bounded non-forking. In addition, we answer a question of Keisler regarding the number of cuts a linear order may have. Namely, we show that it is possible that ded(kappa) < ded(kappa)^omega." @default.
- W4298086144 created "2022-10-01" @default.
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- W4298086144 date "2012-05-14" @default.
- W4298086144 modified "2023-09-29" @default.
- W4298086144 title "On non-forking spectra" @default.
- W4298086144 doi "https://doi.org/10.48550/arxiv.1205.3101" @default.
- W4298086144 hasPublicationYear "2012" @default.
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