English

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 (20)+(2^{\aleph_0})^+. We show, among other things, that the reflection down to <20< 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]].

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}
}