Abstract
In this paper we prove that from large cardinals it is consistent that there is a singular strong limit cardinal such that the singular cardinal hypothesis fails at and every collection of fewer than stationary subsets of reflects simultaneously. For >, this situation was not previously known to be consistent. Using different methods, we reduce the upper bound on the consistency strength of this situation for to below a single partially supercompact cardinal. The previous upper bound of infinitely many supercompact cardinals was due to Sharon.
| Original language | English |
|---|---|
| Pages (from-to) | 1-26 |
| Number of pages | 26 |
| Journal | Journal of Symbolic Logic |
| Volume | 89 |
| Issue number | 1 |
| DOIs | |
| State | Published - 27 Mar 2024 |
Bibliographical note
Publisher Copyright:© The Author(s), 2023. Published by Cambridge University Press on behalf of The Association for Symbolic Logic.
Keywords
- Prikry forcing
- SCH.
- stationary reflection
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