On the existence of universal models
On the existence of universal models
复制标题
论通用模型的存在性
DOI：
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发表时间：
1998
影响因子：
0.3
通讯作者：
S. Shelah
中科院分区：
文献类型：
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作者：
M. Džamonja;S. Shelah
设λ=λ <λ ≥ λ 0，我们考虑一个理论T。本文给出了T的一个判别准则，该判别准则对于T的大小≤λ+的模型，是T的大小为λ+的λ++泛模型一致存在的充分条件，并且当2λ +>λ++时是有意义的.事实上，我们更一般地使用抽象的基本类。共相一致存在的准则适用于各种著名的理论，如无三角形图和简单理论。考虑到在分析中可能的应用，我们进一步观察到，对于这样的λ，对于任何固定的μ>λ+正则，μ=μλ+，2λ=μ是一致的，并且在嵌入h的概念下，不存在大小<μ的λ上的赋范向量空间，这对于λ+维的λ上的赋范向量空间是通用的，其中嵌入h指定（a，B），使得||h（x）/||x∈（a，B）.
Abstract.Suppose that λ=λ <λ ≥ℵ0, and we are considering a theory T. We give a criterion on T which is sufficient for the consistent existence of λ++ universal models of T of size λ+ for models of T of size ≤λ+, and is meaningful when 2λ +>λ++. In fact, we work more generally with abstract elementary classes. The criterion for the consistent existence of universals applies to various well known theories, such as triangle-free graphs and simple theories. Having in mind possible applications in analysis, we further observe that for such λ, for any fixed μ>λ+ regular with μ=μλ+, it is consistent that 2λ=μ and there is no normed vector space over ℚ of size <μ which is universal for normed vector spaces over ℚ of dimension λ+ under the notion of embedding h which specifies (a,b) such that ||h(x)/||x∈(a,b) for all x.