# Global Chang’s Conjecture and singular cardinals

@article{Eskew2021GlobalCC,
title={Global Chang’s Conjecture and singular cardinals},
author={Monroe Eskew and Yair Hayut},
journal={European Journal of Mathematics},
year={2021},
volume={7},
pages={435 - 463}
}
• Published 31 December 2018
• Materials Science
• European Journal of Mathematics
We investigate the possibilities of global versions of Chang’s Conjecture that involve singular cardinals. We show some \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathrm{ZFC}$$\end{document}ZFC limitations on such principles and prove relative to large cardinals that Chang’s Conjecture can consistently hold…
1 Citations
Compactness versus hugeness at successor cardinals
• Mathematics
Journal of Mathematical Logic
• 2022
If $\kappa$ is regular and $2^{<\kappa}\leq\kappa^+$, then the existence of a weakly presaturated ideal on $\kappa^+$ implies $\square^*_\kappa$. This partially answers a question of Foreman and

## References

SHOWING 1-10 OF 37 REFERENCES
The large cardinals between supercompact and almost-huge
The hierarchy of large cardinals between a supercompact cardinal and an almost-huge cardinal is analyzed, and some results relating high-jump cardinals to forcing are proved, as well as analyzing Laver functions for super-high- jump cardinals.
Reflecting stationary sets and successors of singular cardinals
It is shown that supercompactness (and even the failure of PT) implies the existence of non-reflecting stationary sets, and that under suitable assumptions it is consistent that REF and there is a κ which is κ+n-supercompact.
Squares, scales and stationary Reflection
• Mathematics
J. Math. Log.
• 2001
Interactions between these three theories in the context of singular cardinals are considered, focusing on the various implications between square and scales (a fundamental notion in PCF theory), and on consistency results between relatively strong forms of square and stationary set reflection.
When does almost free imply free? (For groups, transversals, etc.)
• Mathematics
• 1994
We show that the construction of an almost free nonfree Abelian group can be pushed from a regular cardinal /C to ~IC+I. Hence there are unboundedly many almost free nonfree Abelian groups below the
A Very Weak Square Principle
• Mathematics
J. Symb. Log.
• 1997
A very weak version of the principle □ discovered by Jensen who proved it holds in the constructible universe L , which is strong enough to include many of the known applications of □, but weak enough that it is consistent with the existence of very large cardinals.
Prikry-Type Forcings
One of the central topics of set theory since Cantor has been the study of the power function κ→2 κ . The basic problem is to determine all the possible values of 2 κ for a cardinal κ. Paul Cohen