Safe Set Theory

This chapter introduces Russell’s idea that sets are built by stages. This avoids the obvious contradictions of the naïve set theory of Cantor’s that stem from situations where it allows some collections, such as \(\{x:x\notin x\}\) , to be “self contradictory sets” as mathematicians referred to them back then when set theory was new and contradictions were first discovered (cf. Wilder 1963).