The pair $(\aleph_n,\aleph_0)$ may fail $\aleph_0$--compactness
Logic
2007-05-23 v1
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.
Keywords
Cite
@article{arxiv.math/0404240,
title = {The pair $(\aleph_n,\aleph_0)$ may fail $\aleph_0$--compactness},
author = {Saharon Shelah},
journal= {arXiv preprint arXiv:math/0404240},
year = {2007}
}