Nakano空间的模泛函与扰动
Modular functionals and perturbations of Nakano spaces
摘要：
我们解决了佩德罗Poitevin \cite{Poitevin:PhD}博士论文中关于中野空间模型论的几个问题。我们首先研究Nakano空间的等距巴拿赫格嵌入，表明在二维及以上的嵌入有一个特别简单和刚性的形式。我们用这个来表明，在巴拿赫格语言的模块功能是可定义的，完整的理论，无原子的中野空间模型完成。我们还证明了直到任意小的扰动指数Nakano空间是$\aleph_0$ -范畴的和$\aleph_0$ -稳定的。特别是它们是稳定的。
英文摘要：
We settle several questions regarding the model theory of Nakano spaces left open by the PhD thesis of Pedro Poitevin \cite{Poitevin:PhD}. We start by studying isometric Banach lattice embeddings of Nakano spaces, showing that in dimension two and above such embeddings have a particularly simple and rigid form. We use this to show show that in the Banach lattice language the modular functional is definable and that complete theories of atomless Nakano spaces are model complete. We also show that up to arbitrarily small perturbations of the exponent Nakano spaces are $\aleph_0$-categorical and $\aleph_0$-stable. In particular they are stable.
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