Forcing with overlapping supercompact extenders
Logic
2021-12-21 v1
Abstract
We build a supercompact version of the forcing defined in \cite{gitik2019}. For each singular cardinal in the ground model with any fixed cofinality, which is a limit of supercompact cardinals, it is possible to force so that the size of the powerset of the singular cardinal is arbitrarily large, while preserving the singular cardinal. An important feature of this forcing is that it is possible to define the forcing so that the successor of the singular cardinal is collapsed, but all the cardinals above it are preserved.
Keywords
Cite
@article{arxiv.2112.10261,
title = {Forcing with overlapping supercompact extenders},
author = {Sittinon Jirattikansakul},
journal= {arXiv preprint arXiv:2112.10261},
year = {2021}
}
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49 pages