Sh:657

• Shelah, S., & Väänänen, J. A. (2000). Stationary sets and infinitary logic. J. Symbolic Logic, 65(3), 1311–1320. arXiv: math/9706225 DOI: 10.2307/2586701 MR: 1791377
• Abstract:
  Let K^0_\lambda be the class of structures \langle\lambda,< ,A\rangle, where A\subseteq\lambda is disjoint from a club, and let K^1_\lambda be the class of structures \langle\lambda,< ,A\rangle, where A\subseteq\lambda contains a club. We prove that if \lambda=\lambda^{< \kappa} is regular, then no sentence of L_{\lambda^+\kappa} separates K^0_\lambda and K^1_\lambda. On the other hand, we prove that if \lambda=\mu^+, \mu=\mu^{< \mu}, and a forcing axiom holds (and \aleph_1^L=\aleph_1 if \mu=\aleph_0), then there is a sentence of L_{\lambda\lambda} which separates K^0_\lambda and K^1_\lambda.
• Version 1997-06-08_11 (13p) published version (11p)

@article{Sh:657,
 author = {Shelah, Saharon and V{\"a}{\"a}n{\"a}nen, Jouko A.},
 title = {{Stationary sets and infinitary logic}},
 journal = {J. Symbolic Logic},
 fjournal = {The Journal of Symbolic Logic},
 volume = {65},
 number = {3},
 year = {2000},
 pages = {1311--1320},
 issn = {0022-4812},
 mrnumber = {1791377},
 mrclass = {03C75 (03E05 03E35 03E50)},
 doi = {10.2307/2586701},
 note = {\href{https://arxiv.org/abs/math/9706225}{arXiv: math/9706225}},
 arxiv_number = {math/9706225}
}