Abstract
The aim of this paper is to apply the approach of Boolean-valued analysis to the theory of injective Banach lattices and to establish the Boolean-valued transfer principle from AL-spaces to injective Banach lattices. We prove that each injective Banach lattice embeds into an appropriate Boolean-valued model, becoming an AL-space. Hence, each theorem about an AL-space within Zermelo–Fraenkel set theory has an analog in the original injective Banach lattice interpreted as a Boolean-valued AL-space. Translation of theorems from AL-spaces to injective Banach lattices is carried out by the appropriate general operations of Boolean-valued analysis.
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