This talk has two parts. In the first part, we will explore some basic aspects of the semantics in Boolean-valued models using tools developed in conditional set theory. The focus will be on Boolean-valued models built from measure algebras. We will describe some basic definitions and theorems in the naive set theory, topology, measure theory, and functional analysis in such models and show with a few examples how such Boolean-valued theorems can be proved from first things and by hand using Boolean reasoning and the exhaustion principle (and without employing a transfer principle). In the second part of the talk, we will interpret some of the internal results of a Boolean-valued model relative to a measure algebra as structures in a standard model, and conversely give some ways how to identify with certain standard objects corresponding objects in a Boolean-valued model. Finally, we will use these connections to give several new applications of Boolean-valued models to the standard model which include examples from ergodic theory, measure theory, and stochastic optimal control. I will also present some open-end questions. The talk will be as much as possible self-contained. This talk is to a large extent based on several published and unpublished joint works with several coauthors.

https://us06web.zoom.us/j/87929792112?pwd=WWNnTkEwOFQwRDdOVXNaK1UzZHBFZz09
Meeting ID: 879 2979 2112
Passcode: 496589