Measurement in Set Theory

Abstract Measurement holds a special place in the epistemology of the physical world. Knowledge that has been verified by measurement is considered more reliable than that deduced from unmeasurable theories. However, relativity shows that the act of measurement is not independent of our frame of reference. From quantum mechanics we learned that the states of some systems cannot be known without a measurement that itself alters the state of that system, and furthermore that there exist certain systems all of whose states we cannot simultaneously know. We propose that certain fundamental functions of set theory are measurements and apply this interpretation to the debate surrounding whether there is a single universe of sets or a multiverse of universes of sets.