subset. For example, being well-ordered is a hereditary property, and so it being finite. If we instantiate in the above schema with "x has cardinality less than κ", we obtain the more general notion of a set being hereditarily of cardinality less than κ, usually denoted by or . We regain the two simple notions we introduced above as being the set of hereditarily finite sets and being the set of hereditarily countable sets. ( is the first uncountable ordinal.) References Graph theory Set theory Model theory Matroid theory ru:Наследственное свойство