# Sh:685

- Džamonja, M., & Shelah, S. (2000).
*On versions of \clubsuit on cardinals larger than \aleph_1*. Math. Japon.,**51**(1), 53–61. arXiv: math/9911228 MR: 1739051 -
Abstract:

We give two results on guessing unbounded subsets of \lambda^+. The first is a positive result and applies to the situation of \lambda regular and at least equal to \aleph_3, while the second is a negative consistency result which applies to the situation of \lambda a singular strong limit with 2^\lambda>\lambda^+. The first result shows that in ZFC there is a guessing of unbounded subsets of S^{\lambda^+}_\lambda. The second result is a consistency result (assuming a supercompact cardinal exists) showing that a natural guessing fails. A result of Shelah in [Sh:667] shows that if 2^\lambda=\lambda^+ and \lambda is a strong limit singular, then the corresponding guessing holds. Both results are also connected to an earlier result of Džamonja-Shelah in which they showed that a certain version of \clubsuit holds at a successor of singular just in ZFC. The first result here shows that a result of [DjSh:545] can to a certain extent be extended to the successor of a regular. The negative result here gives limitations to the extent to which one can hope to extend the mentioned Džamonja-Shelah result. - Version 1999-10-26_10 (17p)

Bib entry

@article{Sh:685, author = {D{\v{z}}amonja, Mirna and Shelah, Saharon}, title = {{On versions of $\clubsuit$ on cardinals larger than $\aleph_1$}}, journal = {Math. Japon.}, fjournal = {Mathematica Japonica}, volume = {51}, number = {1}, year = {2000}, pages = {53--61}, issn = {0025-5513}, mrnumber = {1739051}, mrclass = {03E05 (03E35)}, note = {\href{https://arxiv.org/abs/math/9911228}{arXiv: math/9911228}}, arxiv_number = {math/9911228} }