Syntactic tools related to Δ₁ terms are demonstrated by application to Boolean valued analysis. As an example, the question is considered of what approaches to defining the field R of reals and what complete Boolean algebras B provide the explicit inclusion of R^ into R inside the Boolean-valued universe V(B).

Keywords:set theory, conservative extension, real number, Boolean valued analysis, canonical embedding, σ-distributive Boolean algebra, Σ₁ formula.