# Sh:726

- Shelah, S., & Väänänen, J. A. (2005).
*A note on extensions of infinitary logic*. Arch. Math. Logic,**44**(1), 63–69. arXiv: math/0009080 DOI: 10.1007/s00153-004-0212-8 MR: 2116833 -
Abstract:

We show that a strong form of the so called Lindström’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 Löwenheim-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 Löwenheim-Skolem theorem down to <\kappa. - Version 2001-06-08_11 (10p) published version (7p)

Bib entry

@article{Sh:726, author = {Shelah, Saharon and V{\"a}{\"a}n{\"a}nen, Jouko A.}, title = {{A note on extensions of infinitary logic}}, journal = {Arch. Math. Logic}, fjournal = {Archive for Mathematical Logic}, volume = {44}, number = {1}, year = {2005}, pages = {63--69}, issn = {0933-5846}, mrnumber = {2116833}, mrclass = {03C75 (03C80 03C95)}, doi = {10.1007/s00153-004-0212-8}, note = {\href{https://arxiv.org/abs/math/0009080}{arXiv: math/0009080}}, arxiv_number = {math/0009080} }