# Sh:1135

- Raghavan, D., & Shelah, S. (2019).
*Two results on cardinal invariants at uncountable cardinals*. In Proceedings of the 14th and 15th Asian Logic Conferences, World Sci. Publ., Hackensack, NJ, pp. 129–138. arXiv: 1801.09369 DOI: 10.1142/9789813237551_0006 MR: 3890461 -
Abstract:

We prove two ZFC theorems about cardinal invariants above the continuum which are in sharp contrast to well-known facts about these same invariants at the continuum. It is shown that for an uncoutable regular cardinal \kappa, \mathfrak{b}(\kappa) = \kappa^+ implies \mathfrak{a}(\kappa) = \kappa^+. This improves an earlier result of Blass, Hyttinen and Zhang [3]. It is also shown that if \kappa \ge \beta_\omega is an uncountable regular cardinal, then \mathfrak{d} (\kappa) \le \mathfrak{r}(\kappa). This result partially dualizes an earlier theorem of the authors [6] - published version (6p)

Bib entry

@inproceedings{Sh:1135, author = {Raghavan, Dilip and Shelah, Saharon}, title = {{Two results on cardinal invariants at uncountable cardinals}}, booktitle = {{Proceedings of the 14th and 15th Asian Logic Conferences}}, year = {2019}, pages = {129--138}, publisher = {World Sci. Publ., Hackensack, NJ}, mrnumber = {3890461}, mrclass = {03E17}, doi = {10.1142/9789813237551_0006}, note = {\href{https://arxiv.org/abs/1801.09369}{arXiv: 1801.09369}}, arxiv_number = {1801.09369} }