A Note on Extensions of Infinitary Logic
Logic
2007-05-23 v1
Abstract
We show that a strong form of the so called Lindstrom's Theorem fails to generalize to extensions of L_{kappa,omega} and L_{kappa,kappa}: For weakly compact kappa there is no strongest extension of L_{kappa,omega} with the (kappa,kappa)-compactness property and the Lowenheim-Skolem theorem down to kappa. With an additional set-theoretic assumption, there is no strongest extension of L_{kappa,kappa} with the (kappa,kappa)-compactness property and the Lowenheim-Skolem theorem down to <kappa.
Cite
@article{arxiv.math/0009080,
title = {A Note on Extensions of Infinitary Logic},
author = {Saharon Shelah and Jouko Väänänen},
journal= {arXiv preprint arXiv:math/0009080},
year = {2007}
}