## Journal of Symbolic Logic

### The Existence of Countable Totally Nonconstructive Extensions of the Countable Atomless Boolean Algebra

#### Abstract

Our results concern the existence of a countable extension $\mathscr{U}$ of the countable atomless Boolean algebra $\mathscr{B}$ such that $\mathscr{U}$ is a "nonconstructive" extension of $\mathscr{B}$. It is known that for any fixed admissible indexing $\varphi$ of $\mathscr{B}$ there is a countable nonconstructive extension $\mathscr{U}$ of $\mathscr{B}$ (relative to $\varphi$). The main theorem here shows that there exists an extension $\mathscr{U}$ of $\mathscr{B}$ such that for any admissible indexing $\varphi$ of $\mathscr{B}$, $\mathscr{U}$ is nonconstructive (relative to $\varphi$). Thus, in this sense $\mathscr{U}$ is a countable totally nonconstructive extension of $\mathscr{B}$.

#### Article information

Source
J. Symbolic Logic, Volume 48, Issue 1 (1983), 167-170.

Dates
First available in Project Euclid: 6 July 2007

https://projecteuclid.org/euclid.jsl/1183741200

Mathematical Reviews number (MathSciNet)
MR693258

Zentralblatt MATH identifier
0523.06020

JSTOR