# 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. - published version (17p)

Bib entry

@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} }