# Sh:797

- Shelah, S. (2012).
*Nice infinitary logics*. J. Amer. Math. Soc.,**25**(2), 395–427. arXiv: 1005.2806 DOI: 10.1090/S0894-0347-2011-00712-1 MR: 2869022 -
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} }