Ontology:Q819

Characteristics in draft

item type: Z (wiki feature; pronounced C) 1-1-1
label (en): ZFC set theory 1-1-1
alias (en): Zermelo-Fraenkel Choice-axiom set theory (ZFC); ZFC (set theory)
external identifier: Zermelo-Fraenkel set theory
sub-case of [Item]: set theory (top-level category) 1-1-1
case of: field of mathematics
prototype notes: set theory where sets are "computational" and pointers into the set cause a kind of infinite loop bug in the logic

model combines claims: [S2] Sets are collections of unique objects / Set cardinality measures a set's number of elements which are unique and partly defines the set
model combines claims: [Z2] Sets are equal if they contain all of the same unique elements / axiom of extensionality
model combines claims: [S2] Sets can contain other sets
model combines claims: [S2] Sets cannot contain themselves / Every non-empty set contains a member which makes it not equivalent to itself / axiom of regularity
model combines claims: [Z2] Every element in a set is a set / No element in a set is an atom (atomic data structure)
model combines claims: [Z2] Any two sets can join into a greater set / For any two sets there can be a set containing them / axiom of pairing
model combines claims: [S2] Any element in a set can represent the whole set / When constructing a new set out of one element from each set it does not matter which one is used / AC (axiom of choice)