## Journal of Symbolic Logic

### A Model in which the Base-Matrix Tree Cannot have Cofinal Branches

Peter Lars Dordal

#### Abstract

A model of ZFC is constructed in which the distributivity cardinal $\mathbf{h}$ is $2^{\aleph_0} = \aleph_2$, and in which there are no $\omega_2$-towers in $\lbrack\omega\rbrack^\omega$. As an immediate corollary, it follows that any base-matrix tree in this model has no cofinal branches. The model is constructed via a form of iterated Mathias forcing, in which a mixture of finite and countable supports is used.

#### Article information

Source
J. Symbolic Logic, Volume 52, Issue 3 (1987), 651-664.

Dates
First available in Project Euclid: 6 July 2007

https://projecteuclid.org/euclid.jsl/1183742433

Mathematical Reviews number (MathSciNet)
MR902981

Zentralblatt MATH identifier
0637.03049

JSTOR

#### Citation

Dordal, Peter Lars. A Model in which the Base-Matrix Tree Cannot have Cofinal Branches. J. Symbolic Logic 52 (1987), no. 3, 651--664. https://projecteuclid.org/euclid.jsl/1183742433