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Preprint Number 567

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Moran Cohen, Saharon Shelah
Ranks for strongly dependent theories

Submission date: 15 March 2013


There is much more known about the family of superstable theories when compared to stable theories. This calls for a search of an analogous “super-dependent” characterization in the context of dependent theories. This problem has been treated in [Sh:783,Sh:863], where the candidates “Strongly dependent”, “Strongly dependent^2” and others were considered. These families generated new families when we are considering intersections with the stable family. Here, continuing \S2, \S 5E,F,G][Sh:863], we deal with several candidates, defined using dividing properties and related ranks of types. Those candidates are subfamilies of “Strongly dependent”. Fulfilling some promises from [Sh:863] in particular [1.4(4)][Sh:863], we try to make this self contained within reason by repeating some things from there. More specifically we fulfil some promises from [Sh:863] to give more details, in particular: in \S4 for [1.4(4)][Sh:863], in \S2 for [5.47(2)=Ldw5.35(2)][Sh:863] and in \S1 for [5.49(2)][Sh:863].

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Full text arXiv 1303.3441: pdf, ps.

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