Ontology:Q819

1. ZFC set theory 1:(-)1:(-)1

Characteristics in draft

Properties

item type

Z (wiki feature; C (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

Components

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)

Wavebuilder combinations

[P] (pronounced [P]) Wavebuilder (pronounced Wavebuilder): forms result [Item]

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along with [Item]

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forming from [Item]

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