# 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)

Bib entry

@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} }