# 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. - published version (11p)

Bib entry

@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}, doi = {10.2307/2586701}, mrclass = {03C75 (03E05 03E35 03E50)}, mrnumber = {1791377}, mrreviewer = {Andreas Blass}, doi = {10.2307/2586701}, note = {\href{https://arxiv.org/abs/math/9706225}{arXiv: math/9706225}}, arxiv_number = {math/9706225} }