A hierarchy of hereditarily finite sets

This article defines a hierarchy on the hereditarily finite sets which reflects the way sets are built up from the empty set by repeated adjunction, the addition to an already existing set of a single new element drawn from the already existing sets. The structure of the lowest levels of this hierarchy is examined, and some results are obtained about the cardinalities of levels of the hierarchy. Keywords Finite set theory

• Type: Journal
• Year: 2008
• Where: AML
• Authors: Laurence Kirby
• Keywords: AML 2008, Hereditarily Finite Sets, Lowest Levels, Mathematics Subject Classification