English

Stationary reflection principles and two cardinal tree properties

Logic 2014-10-29 v1

Abstract

We study consequences of stationary and semi-stationary set reflection. We show that the semi stationary reflection principle implies the Singular Cardinal Hypothesis, the failure of weak square principle, etc. We also consider two cardinal tree properties introduced recently by Weiss and prove that they follow from stationary and semi stationary set reflection augmented with a weak form of Martin's Axiom. We also show that there are some differences between the two reflection principles which suggest that stationary set reflection is analogous to supercompactness whereas semi-stationary set reflection is analogous to strong compactness.

Keywords

Cite

@article{arxiv.1301.7528,
  title  = {Stationary reflection principles and two cardinal tree properties},
  author = {Hiroshi Sakai and Boban Velickovic},
  journal= {arXiv preprint arXiv:1301.7528},
  year   = {2014}
}

Comments

19 pages

R2 v1 2026-06-21T23:18:24.607Z