## Journal of Symbolic Logic

### Larger Cardinals in Cichon's Diagram

Jorg Brendle

#### Abstract

We prove that in many situations it is consistent with ZFC that part of the invariants involved in Cichon's diagram are equal to $\kappa$ while the others are equal to $\lambda$, where $\kappa < \lambda$ are both arbitrary regular uncountable cardinals. We extend some of these results to the case when $\lambda$ is singular. We also show that $\mathrm{cf}(\kappa_U(\mathscr{L})) < \kappa_A(\mathscr{M})$ is consistent with ZFC.

#### Article information

Source
J. Symbolic Logic, Volume 56, Issue 3 (1991), 795-810.

Dates
First available in Project Euclid: 6 July 2007

Permanent link to this document
https://projecteuclid.org/euclid.jsl/1183743728

Digital Object Identifier
doi:10.2178/jsl/1183743728

Mathematical Reviews number (MathSciNet)
MR1129144

Zentralblatt MATH identifier
0758.03021

JSTOR
links.jstor.org

#### Citation

Brendle, Jorg. Larger Cardinals in Cichon's Diagram. J. Symbolic Logic 56 (1991), no. 3, 795--810. doi:10.2178/jsl/1183743728. https://projecteuclid.org/euclid.jsl/1183743728