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Dependent first order theories, continued

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Abstract

A dependent theory is a (first order complete theory) T which does not have the independence property. A major result here is: if we expand a model of T by the traces on it of sets definable in a bigger model then we preserve its being dependent. Another one justifies the cofinality restriction in the theorem (from a previous work) saying that pairwise perpendicular indiscernible sequences, can have arbitrary dual-cofinalities in some models containing them. We introduce “strongly dependent” and look at definable groups; and also at dividing, forking and relatives.

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Correspondence to Saharon Shelah.

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The author would like to thank the Israel Science Foundation for partial support of this research (Grant No. 242/03). Publication 783.

I would like to thank Alice Leonhardt for the beautiful typing. Received June 18, 2004 and in revised form October 5, 2006

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Shelah, S. Dependent first order theories, continued. Isr. J. Math. 173, 1–60 (2009). https://doi.org/10.1007/s11856-009-0082-1

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  • DOI: https://doi.org/10.1007/s11856-009-0082-1

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