Strongly dependent theories
Strongly dependent theories
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强相关理论
DOI：
10.1007/s11856-014-1111-2
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发表时间：
2005
影响因子：
1
通讯作者：
S. Shelah
中科院分区：
文献类型：
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作者：
S. Shelah
本文继续[Sh：715]，[Sh：783]及相关工作，进一步研究了强相依（一阶完备）理论T的模型类.这些性质（=类）在某种程度上与稳定理论中的超稳定性平行，尽管它们甚至对于稳定理论也是不同的。我们证明了它们的一些定义的等价性，研究了相关的秩，并给出了一些例子，例如，p-ADIC的一阶理论是强相关的。最显著的结果是：如果|一| + |不|≤ μ，I ≤ μ，|我|≥ℶ|不|+（μ），则某个基数μ+的J I是A上的不可分辨序列。
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 ⊆ ℭ and |I|≥ℶ|T|+(µ), then some J ⊆ I of cardinality µ+ is an indiscernible sequence over A.