# 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. - No downloadable versions available.

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} }