Sh:835
- Shelah, S. (2024). pcf without choice Sh835. Arch. Math. Logic, 63(5-6), 623–654. arXiv: math/0510229 DOI: 10.1007/s00153-023-00900-7 MR: 4765805
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Abstract:
We mainly investigate models of set theory with restricted choice, e.g., ZF + DC + the family of countable subsets of \lambda is well ordered for every \lambda (really local version for a given \lambda). We think that in this frame much of pcf theory, (and combinatorial set theory in general) can be generalized. We prove here, in particular, that there is a proper class of regular cardinals, every large enough successor of singular is not measurable and we can prove cardinal inequalities.Solving some open problems, we prove that if \mu > \kappa = cf(\mu) > \aleph_{0}, then from a well ordering of P(P(\kappa)) \cup {}^{\kappa >} \mu we can define a well ordering of {}^{\kappa} \mu.
- Version 2023-11-20 (32p)
Bib entry
@article{Sh:835,
author = {Shelah, Saharon},
title = {{pcf without choice Sh835}},
journal = {Arch. Math. Logic},
fjournal = {Archive for Mathematical Logic},
volume = {63},
number = {5-6},
year = {2024},
pages = {623--654},
issn = {0933-5846},
mrnumber = {4765805},
mrclass = {03E25 (03E04)},
doi = {10.1007/s00153-023-00900-7},
note = {\href{https://arxiv.org/abs/math/0510229}{arXiv: math/0510229}},
arxiv_number = {math/0510229}
}