# Sh:604

• Shelah, S. (2005). The pair (\aleph_n,\aleph_0) may fail \aleph_0-compactness. In Logic Colloquium ’01, Vol. 20, Assoc. Symbol. Logic, Urbana, IL, pp. 402–433.
• Abstract:
Let P be a distinguished unary predicate and K=\{M: M a model of cardinality \aleph_n with P^M of cardinality \aleph_0\}. We prove that consistently for n=4, for some countable first order theory T we have: T has no model in K whereas every finite subset of T has a model in K. We then show how we prove it also for n=2, too.
Bib entry
@incollection{Sh:604,
author = {Shelah, Saharon},
title = {{The pair $(\aleph_n,\aleph_0)$ may fail $\aleph_0$-compactness}},
booktitle = {{Logic Colloquium '01}},
series = {Lect. Notes Log.},
volume = {20},
year = {2005},
pages = {402--433},
mrclass = {03E02 (03C55 03E35 03E50)},
mrnumber = {2143906},
mrreviewer = {Mirna D\v{z}amonja},
publisher = {Assoc. Symbol. Logic, Urbana, IL},
note = {\href{https://arxiv.org/abs/math/0404240}{arXiv: math/0404240}},
arxiv_number = {math/0404240}
}