# Sh:484

• Liu, K., & Shelah, S. (1997). Cofinalities of elementary substructures of structures on \aleph_\omega. Israel J. Math., 99, 189–205.
• 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)
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}
}