## Journal of Symbolic Logic

### Why Solovay Real Produces Cohen Real

Janusz Pawlikowski

#### Abstract

An explanation is given of why, after adding to a model $M$ of ZFC first a Solovay real $r$ and next a Cohen real $c$, in $M\lbrack r\rbrack\lbrack c\rbrack$ a Cohen real over $M\lbrack c\rbrack$ is produced. It is also shown that a Solovay algebra iterated with a Cohen algebra can be embedded into a Cohen algebra iterated with a Solovay algebra.

#### Article information

Source
J. Symbolic Logic, Volume 51, Issue 4 (1986), 957-968.

Dates
First available in Project Euclid: 6 July 2007

Permanent link to this document
https://projecteuclid.org/euclid.jsl/1183742234

Mathematical Reviews number (MathSciNet)
MR865922

Zentralblatt MATH identifier
0622.03036

JSTOR