Strong downward Löwenheim-Skolem theorems for stationary logics, III -- mixed support iteration

2021/07/06 by Sakaé Fuchino, Fuchino, Sakaé, André Ottenbreit Maschio Rodrigue +3 · 1 citation
Computer Science · Decision Sciences · Mathematics · #03E35 #03E55 #03E65 #03E75 #05C63 #54E35 #Advanced Algebra and Logic #Advanced Topology and Set Theory #FOS: Mathematics #Fuzzy and Soft Set Theory #Logic (math.LO)

paper · pdf · doi:10.48550/arxiv.2107.02577

openalex publication_date 2021/07/06 · openalex created_date 2021/07/19 · openalex updated_date 2026/07/28

Abstract

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^ℵ₀)⁺. We show, among other things, that the reflection down to < 2^ℵ₀ 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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