Strongly dependent theories |
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Authors: | Saharon Shelah |
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Institution: | 1. Einstein Institute of Mathematics, The Hebrew University of Jerusalem, Edmond J. Safra Campus, Givat Ram, Jerusalem, 91904, Israel 2. Department of Mathematics, Hill Center-Busch Campus, Rutgers, The State University of New Jersey, 110 Frelinghuysen Road, Piscataway, NJ, 08854-8019, USA
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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 (= classes) somewhat parallel to superstability among stable theory, though are different from it even for stable theories. We show 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: if |A| + |T| ≤ µ, I ? ? and |I|≥?|T|+(µ), then some J ? I of cardinality µ+ is an indiscernible sequence over A. |
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