Sh:484

• Liu, K., & Shelah, S. (1997). Cofinalities of elementary substructures of structures on $\aleph_\omega$. Israel J. Math., 99, 189–205. arXiv: math/9604242 DOI: 10.1007/BF02760682 MR: 1469093
• Abstract:
  Let $0<n^*<\omega$ and $f:X\to n^*+1$ be a function where $X\subseteq\omega\backslash (n^*+1)$ is infinite. Consider the following set $S_f=\{x\subset\aleph_\omega: |x|\le\aleph_{n^*}\ \& \ (\forall n\in X)cf(x\cap\alpha_n)=\aleph_{f(n)}\}$. The question, first posed by Baumgartner, is whether $S_f$ is stationary in $[\alpha_\omega]^{<\aleph_{n^*+1}}$. By a standard result, the above question can also be rephrased as certain transfer property. Namely, $S_f$ is stationary iff for any structure $A=\langle\aleph_\omega, \ldots\rangle$ there’s a $B\prec A$ such that $|B|=\aleph_{n^*}$ and for all $n\in X$ we have $cf(B\cap\aleph_n)=\aleph_{f(n)}$. In this paper, we are going to prove a few results concerning the above question.
• Version 1996-04-19_10 (13p) published version (17p)

@article{Sh:484,
 author = {Liu, Kecheng and Shelah, Saharon},
 title = {{Cofinalities of elementary substructures of structures on $\aleph_\omega$}},
 journal = {Israel J. Math.},
 fjournal = {Israel Journal of Mathematics},
 volume = {99},
 year = {1997},
 pages = {189--205},
 issn = {0021-2172},
 mrnumber = {1469093},
 mrclass = {03E05 (03C55 04A20 04A30)},
 doi = {10.1007/BF02760682},
 note = {\href{https://arxiv.org/abs/math/9604242}{arXiv: math/9604242}},
 arxiv_number = {math/9604242}
}