Caltech/UCLA Joint Analysis Seminar

The aim of this talk is to provide an introduction to Boolean-valued analysis which refers to the application of Boolean-valued models to analysis. We focus on Boolean-valued models that are built from a sigma-finite measure space. We will discuss how basic Boolean-valued structures such as real numbers, vector spaces, and compact spaces are interpreted in standard analysis, and how certain objects in standard analysis and probability such as function spaces, Hilbert bundles, and conditional expectations can be translated to a Boolean-valued context. We build a bridge between classical functional analysis and Boolean-valued functional analysis via vector duality. As one major application, we present the use of Boolean-valued models to systematically preserve measurability and conditioning. No knowledge of mathematical logic is required.