平稳逻辑的强向下Löwenheim-Skolem定理，III --混合支撑迭代
Strong downward Löwenheim-Skolem theorems for stationary logics, III -- mixed support iteration
摘要：
继续[Fuchino，Ottenbreit and Sakai[9，10]]和[Fuchino and Ottenbreit[11]]，我们进一步研究了与平稳逻辑的Löwenheim-Skolem定理有关的反射原理。本文主要分析了在一个超紧长度的混合支集迭代中，通过坍缩另一个超紧基数得到$(2^{\aleph_0})^+$的情形。我们证明了，除其他事项外，具有小特征的拓扑空间的不可度量化的下至$< 2^{\aleph_0}$的反射与[Fuchino，Ottenbreit和Sakai[9，10]]和[Fuchino和Ottenbreit[11]]中研究的反射性质无关。
英文摘要：
Continuing [Fuchino, Ottenbreit and Sakai[9, 10]] and [Fuchino and Ottenbreit[11]], we further study reflection principles in connection with the Löwenheim-Skolem Theorems of stationary logics. In this paper, we mainly analyze the situations in the models obtained by mixed support iteration of a supercompact length and then collapsing another supercompact cardinal to make it $(2^{\aleph_0})^+$. We show, among other things, that the reflection down to $< 2^{\aleph_0}$ of the non-metrizability of topological spaces with small character is independent from the reflection properties studied in [Fuchino, Ottenbreit and Sakai[9, 10]] and [Fuchino and Ottenbreit[11]].
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