Journal of Symbolic Logic

Boolean Universes above Boolean Models

Friedrich Wehrung

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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

Permanent link to this document
https://projecteuclid.org/euclid.jsl/1183744372

Mathematical Reviews number (MathSciNet)
MR1253919

Zentralblatt MATH identifier
0793.03045

JSTOR
links.jstor.org

Subjects
Primary: 03C90: Nonclassical models (Boolean-valued, sheaf, etc.)
Secondary: 08a45 06F05: Ordered semigroups and monoids [See also 20Mxx] 06f20 54H99: None of the above, but in this section

Keywords
Atoms Boolean models first-order languages convergence in lattice-ordered rings equational compactness algebraic compactness

Citation

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


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