# Introduction to continuous logic

Boise Set Theory Seminar, Boise, March 2015

*Abstract*: Continous logic is a proper generalization of first order logic where the usual binary truth values are replaced by the unit interval $[0,1]$. The models for this logic are metric structures, which are metric spaces together with continuous functions and $[0,1]$-valued relations. Just as ordinary logic has typical applications in discrete math, continuous logic has applications in analysis. In this talk we will introduce just the basic concepts and theory of continuous logic.