Sh:863
- Shelah, S. (2014). Strongly dependent theories. Israel J. Math., 204(1), 1–83. arXiv: math/0504197 DOI: 10.1007/s11856-014-1111-2 MR: 3273451
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Abstract:
We further investigate the class of models of a strongly dependent (first-order complete) theory T, continuing [Sh:715], [Sh:783], and related works. Those are properties (equivalently, classes) somewhat analogous to superstability among stable theories, although there are differences even in the stable case. We show the equivalence of some of their definitions, investigate relevant ranks and give some examples: e.g. the first-order theory of the p-adics is strongly dependent.The most notable result is the following: if |A| + |T| \le \mu, \mathbf{I} \subseteq \mathfrak{C}, and |\mathbf{I}| \ge \beth_{|T|^+}(\mu) then some \mathbf{J} \subseteq \mathbf{I} of cardinality \mu^+ is an indiscernible sequence over A.
- Version 2024-11-03 (76p) published version (83p)
Bib entry
@article{Sh:863,
author = {Shelah, Saharon},
title = {{Strongly dependent theories}},
journal = {Israel J. Math.},
fjournal = {Israel Journal of Mathematics},
volume = {204},
number = {1},
year = {2014},
pages = {1--83},
issn = {0021-2172},
mrnumber = {3273451},
mrclass = {03C45},
doi = {10.1007/s11856-014-1111-2},
note = {\href{https://arxiv.org/abs/math/0504197}{arXiv: math/0504197}},
arxiv_number = {math/0504197}
}