## Bulletin of Symbolic Logic

### Relations between Some Cardinals in the Absence of the Axiom of Choice

#### Abstract

If we assume the axiom of choice, then every two cardinal numbers are comparable, In the absence of the axiom of choice, this is no longer so. For a few cardinalities related to an arbitrary infinite set, we will give all the possible relationships between them, where possible means that the relationship is consistent with the axioms of set theory. Further we investigate the relationships between some other cardinal numbers in specific permutation models and give some results provable without using the axiom of choice.

#### Article information

Source
Bull. Symbolic Logic, Volume 7, Number 2 (2001), 237-261.

Dates
First available in Project Euclid: 20 June 2007

https://projecteuclid.org/euclid.bsl/1182353777

Mathematical Reviews number (MathSciNet)
MR1839547

Zentralblatt MATH identifier
1001.03041

JSTOR

#### Citation

Halbeisen, Lorenz; Shelah, Saharon. Relations between Some Cardinals in the Absence of the Axiom of Choice. Bull. Symbolic Logic 7 (2001), no. 2, 237--261. https://projecteuclid.org/euclid.bsl/1182353777