The Logic of Comparative Cardinality

Author(s): Ding, Yifeng; Harrison-Trainor, Matthew; Holliday, Wesley Halcrow | Abstract: This paper investigates the principles that one must add to Boolean algebra to capture reasoning not only about intersection, union, and omplementation of sets, but also about the relative size of sets. We completely axiomatize such reasoning under the Cantorian definition of relative size in terms of injections.