Sh:775
- Shelah, S. (2005). Super black box (ex. Middle diamond). Arch. Math. Logic, 44(5), 527–560. arXiv: math/0212249 DOI: 10.1007/s00153-004-0239-x MR: 2210145
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Abstract:
This is a slightly corrected version of an old work.Under certain cardinal arithmetic assumptions, we prove that for every large enough regular \lambda cardinal, for many regular \kappa < \lambda, many stationary subsets of \lambda concentrating on cofinality \kappa have super BB. In particular, we have the super BB on \{\delta < \lambda \colon cf(\delta) = \kappa\}. This is a strong negation of uniformization.
We have added some details. Works continuing it are [Sh:898] and [Sh:1028]. We thank Ari Brodski and Adi Jarden for their helpful comments.
In this paper we had earlier used the notion “middle diamond" which is now replaced by “super BB”, that is, “super black box”, in order to be consistent with other papers (see [Sh:898]).
- Version 2023-05-01_2 (39p) published version (34p)
Bib entry
@article{Sh:775,
author = {Shelah, Saharon},
title = {{Super black box (ex. Middle diamond)}},
journal = {Arch. Math. Logic},
fjournal = {Archive for Mathematical Logic},
volume = {44},
number = {5},
year = {2005},
pages = {527--560},
issn = {0933-5846},
mrnumber = {2210145},
mrclass = {03E05 (03E10 03E50 03E55)},
doi = {10.1007/s00153-004-0239-x},
note = {\href{https://arxiv.org/abs/math/0212249}{arXiv: math/0212249}},
arxiv_number = {math/0212249}
}