# Sh:797

• Shelah, S. (2012). Nice infinitary logics. J. Amer. Math. Soc., 25(2), 395–427.
• Abstract:
We deal with soft model theory of infinitary logics. We find a logic between {mathbb L}_{\infty,\aleph_0} and {\mathbb L}_{\infty, \infty} which has some striking properties. First, it has interpolations (it was known that each of those logics fail interpolation though the pair has). Second, well ordering is not characterized in a strong way. Third, it can be characterized as the maximal such nice logic (in fact, is the maximal logic stronger than {\mathbb L}_{\infty, \aleph_0} and which satisfies “well ordering is not characterized in a strong way").
• Version 2014-08-20_12 (36p) published version (33p)
Bib entry
@article{Sh:797,
author = {Shelah, Saharon},
title = {{Nice infinitary logics}},
journal = {J. Amer. Math. Soc.},
fjournal = {Journal of the American Mathematical Society},
volume = {25},
number = {2},
year = {2012},
pages = {395--427},
issn = {0894-0347},
mrnumber = {2869022},
mrclass = {03C95 (03C55 03C80)},
doi = {10.1090/S0894-0347-2011-00712-1},
note = {\href{https://arxiv.org/abs/1005.2806}{arXiv: 1005.2806}},
arxiv_number = {1005.2806}
}