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. arXiv: math/0404240 MR: 2143906
• 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.
• Version 2005-08-03_10 (43p) published version (32p)

@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},
 publisher = {Assoc. Symbol. Logic, Urbana, IL},
 mrnumber = {2143906},
 mrclass = {03E02 (03C55 03E35 03E50)},
 note = {\href{https://arxiv.org/abs/math/0404240}{arXiv: math/0404240}},
 arxiv_number = {math/0404240}
}