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arXiv · 2107.02577

Strong downward L\"owenheim-Skolem theorems for stationary logics, III -- mixed support iteration

Sakaé Fuchino·André Ottenbreit Maschio Rodrigue·Hiroshi Sakai
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Abstract

Continuing [Fuchino, Ottenbreit and Sakai[9, 10]] and [Fuchino and Ottenbreit[11]], we further study reflection principles in connection with the L\"owenheim-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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Sakaé Fuchino, André Ottenbreit Maschio Rodrigue, Hiroshi Sakai. 2021-07-06. Strong downward L\"owenheim-Skolem theorems for stationary logics, III -- mixed support iteration. https://arxiv.org/abs/2107.02577

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