The length of a subset of the real line can be defined in mathematical terms. A set of real numbers is called "measurable" if a precise, definite length can be assigned to it, following certain desired natural properties. Surprisingly, from the axioms of Set Theory we can show the
existence of sets that are not measurable, somewhat violating our physical intuition of the notion of length in space. A natural logical question arises: can some axioms of Set Theory be replaced by different axioms that not only prohibit the existence of the pathological sets just
mentioned, but guarantee that every set is measurable? In this talk we will explore this possibility, and in this process we will explain the connection between infinite-length games, sets of real numbers and infinite trees.
This talk is mostly self contained. Only some basic knowledge of Real Analysis will be assumed.