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DOI: 10.23671/VNC.2012.14.10953

# 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
For citation: Gutman A. E. An example of using $$\Delta_1$$ terms in boolean valued analysis. Vladikavkazskii matematicheskii zhurnal [Vladikavkaz Math. J.], 2012, vol. 14, no. 1, pp. 47-63. DOI 10.23671/VNC.2012.14.10953