## Journal of Symbolic Logic

### Boolean Universes above Boolean Models

Friedrich Wehrung

#### Abstract

We establish several first- or second-order properties of models of first-order theories by considering their elements as atoms of a new universe of set theory and by extending naturally any structure of Boolean model on the atoms to the whole universe. For example, complete $f$-rings are "boundedly algebraically compact" in the language $(+,-,\cdot,\wedge,\vee,\leq)$, and the positive cone of a complete $l$-group with infinity adjoined is algebraically compact in the language $(+, \vee, \leq)$. We also give an example with any first-order language. The proofs can be translated into "naive set theory" in a uniform way.

#### Article information

Source
J. Symbolic Logic, Volume 58, Issue 4 (1993), 1219-1250.

Dates
First available in Project Euclid: 6 July 2007

https://projecteuclid.org/euclid.jsl/1183744372

Mathematical Reviews number (MathSciNet)
MR1253919

Zentralblatt MATH identifier
0793.03045

JSTOR

#### Citation

Wehrung, Friedrich. Boolean Universes above Boolean Models. J. Symbolic Logic 58 (1993), no. 4, 1219--1250. https://projecteuclid.org/euclid.jsl/1183744372