Sh:587

• Shelah, S. (2003). Not collapsing cardinals \leq\kappa in (<\kappa)-support iterations. Israel J. Math., 136, 29–115. arXiv: math/9707225 DOI: 10.1007/BF02807192 MR: 1998104
• Abstract:
  We deal with the problem of preserving various versions of completeness in (<\kappa)–support iterations of forcing notions, generalizing the case “S–complete proper is preserved by CS iterations for a stationary co-stationary S\subseteq\omega_1”. We give applications to Uniformization and the Whitehead problem. In particular, for a strongly inaccessible cardinal \kappa and a stationary set S\subseteq\kappa with fat complement we can have uniformization for \langle A_\delta:\delta\in S'\rangle, A_\delta \subseteq\delta=\sup A_\delta, cf(\delta)=otp(A_\delta) and a stationary non-reflecting set S'\subseteq S.
• Version 2001-11-12_11 (67p) published version (87p)

@article{Sh:587,
 author = {Shelah, Saharon},
 title = {{Not collapsing cardinals $\leq\kappa$ in $(<\kappa)$-support iterations}},
 journal = {Israel J. Math.},
 fjournal = {Israel Journal of Mathematics},
 volume = {136},
 year = {2003},
 pages = {29--115},
 issn = {0021-2172},
 mrnumber = {1998104},
 mrclass = {03E35 (03E05 03E40)},
 doi = {10.1007/BF02807192},
 note = {\href{https://arxiv.org/abs/math/9707225}{arXiv: math/9707225}},
 arxiv_number = {math/9707225}
}