Editing Principia Mathematica (section)

===Part III Cardinal arithmetic. Volume II ✱100 to ✱126===

This covers the definition and basic properties of cardinals. A cardinal is defined to be an equivalence class of similar classes (as opposed to [[Zermelo–Fraenkel set theory|ZFC]], where a cardinal is a special sort of von Neumann ordinal). Each type has its own collection of cardinals associated with it, and there is a considerable amount of bookkeeping necessary for comparing cardinals of different types. PM define addition, multiplication and exponentiation of cardinals, and compare different definitions of finite and infinite cardinals. ✱120.03 is the Axiom of infinity.