Journal of Symbolic Logic

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

E. W. Madison

Full-text is available via JSTOR, for JSTOR subscribers. Go to this article in JSTOR.

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

Permanent link to this document
https://projecteuclid.org/euclid.jsl/1183741200

Mathematical Reviews number (MathSciNet)
MR693258

Zentralblatt MATH identifier
0523.06020

JSTOR
links.jstor.org

Citation

Madison, E. W. The Existence of Countable Totally Nonconstructive Extensions of the Countable Atomless Boolean Algebra. J. Symbolic Logic 48 (1983), no. 1, 167--170. https://projecteuclid.org/euclid.jsl/1183741200


Export citation