Strong downward L\"owenheim-Skolem theorems for stationary logics, III -- mixed support iteration
Logic
2021-07-07 v1
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 . We show, among other things, that the reflection down to 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]].
Keywords
Cite
@article{arxiv.2107.02577,
title = {Strong downward L\"owenheim-Skolem theorems for stationary logics, III -- mixed support iteration},
author = {Sakaé Fuchino and André Ottenbreit Maschio Rodrigue and Hiroshi Sakai},
journal= {arXiv preprint arXiv:2107.02577},
year = {2021}
}