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What (who) is hereditarily$34810$ - definition
Pure countable set; Hereditarily countable
Hereditarily countable set
In set theory, a set is called hereditarily countable if it is a countable set of hereditarily countable sets. This inductive definition is well-founded and can be expressed in the language of first-order set theory.
Hereditarily finite set
FINITE SETS WHOSE ELEMENTS ARE ALL HEREDITARILY FINITE SETS
Hereditarily finite; Hereditarily finite sets; Pure finite set; Ackermann coding; Ackermann encoding
In mathematics and set theory, hereditarily finite sets are defined as finite sets whose elements are all hereditarily finite sets. In other words, the set itself is finite, and all of its elements are finite sets, recursively all the way down to the empty set.
Permutation model
MODEL OF SET THEORY CONSTRUCTED USING PERMUTATIONS
Symmetric model; Hereditarily symmetric set
In mathematical set theory, a permutation model is a model of set theory with atoms (ZFA) constructed using a group of permutations of the atoms. A symmetric model is similar except that it is a model of ZF (without atoms) and is constructed using a group of permutations of a forcing poset.
Wikipedia
Hereditarily countable set
In set theory, a set is called hereditarily countable if it is a countable set of hereditarily countable sets.
