An example of using \(\Delta_1\) terms in boolean valued analysis

Gutman A. E.
Vladikavkaz Mathematical Journal 2012. Vol. 14. Issue 1.

Abstract:
Syntactic tools related to \(\Delta_1\) terms  are demonstrated by application to Boolean valued analysis.  As an example, the question is considered of what approaches to defining the field \(\mathbb R\) of reals  and what complete Boolean algebras \(B\)  provide the explicit inclusion \(\mathbb R^{\scriptscriptstyle\land}\!\subset\mathbb R\)  inside the Boolean valued universe  \(\mathbb V^{(\mskip-3mu B\mskip-2mu)}\).

Keywords: set theory, conservative extension, real number, Boolean valued analysis, canonical embedding, \(\sigma\)-distributive Boolean algebra, \(\Sigma_1\) formula

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