ZF
E84442
ZF is the standard axiomatic framework for set theory that underpins much of modern mathematics.
All labels observed (2)
How this entity was disambiguated
This entity first appeared as the object of triple T694028 — resolving that mention is where its identity was fixed. The disambiguator weighed these candidate entities and picked the highlighted one (or “None”, minting a new entity). This is how homonymy is resolved: the same surface form can point to different entities.
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: ZF Context triple: [Zermelo–Fraenkel set theory, abbreviation, ZF]
-
A.
Z
Z is the neutral elementary particle known as the Z boson, a carrier of the weak nuclear force in the Standard Model of particle physics.
-
B.
ZZ
ZZ is an aircraft registration prefix used to identify certain aircraft, such as those in the Voyager KC2 fleet.
-
C.
ZH
ZH is the official vehicle registration code used for the Swiss canton of Zurich.
-
D.
MZ
MZ is the two-letter ISO 3166-1 alpha-2 country code assigned to Mozambique.
-
E.
ZWN
ZWN is a former currency code used to denote an early version of the Zimbabwean dollar in international financial and foreign exchange contexts.
- F. None of above. chosen
- G. Unsure - the case is ambiguous/there is not enough information to decide.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: ZF Target entity description: ZF is the standard axiomatic framework for set theory that underpins much of modern mathematics.
-
A.
Z
Z is the neutral elementary particle known as the Z boson, a carrier of the weak nuclear force in the Standard Model of particle physics.
-
B.
ZZ
ZZ is an aircraft registration prefix used to identify certain aircraft, such as those in the Voyager KC2 fleet.
-
C.
ZH
ZH is the official vehicle registration code used for the Swiss canton of Zurich.
-
D.
MZ
MZ is the two-letter ISO 3166-1 alpha-2 country code assigned to Mozambique.
-
E.
ZWN
ZWN is a former currency code used to denote an early version of the Zimbabwean dollar in international financial and foreign exchange contexts.
- F. None of above. chosen
Statements (48)
| Predicate | Object |
|---|---|
| instanceOf |
axiomatic set theory
ⓘ
first-order theory ⓘ formal system ⓘ |
| allowsConstructionOf |
complex numbers
ⓘ
integers ⓘ natural numbers ⓘ rational numbers ⓘ real numbers ⓘ |
| assumes | all mathematical objects are sets ⓘ |
| consistencyQuestion | relative to large cardinal axioms ⓘ |
| developedInCentury | 20th century ⓘ |
| differsFrom |
ZFC
ⓘ
linked to:
ZF
|
| extends | Zermelo set theory ⓘ |
| field |
mathematical logic
ⓘ
set theory ⓘ |
| fullName | Zermelo–Fraenkel set theory ⓘ |
| hasAxiom |
axiom of empty set
ⓘ
axiom of extensionality ⓘ axiom of foundation ⓘ axiom of infinity ⓘ axiom of pairing ⓘ axiom of power set ⓘ axiom of union ⓘ axiom schema of replacement ⓘ axiom schema of separation ⓘ |
| hasAxiomSchema |
replacement
ⓘ
separation ⓘ |
| hasCumulativeHierarchy | von Neumann universe ⓘ |
| hasModelType |
countable model
ⓘ
transitive model ⓘ |
| hasNonLogicalSymbol | binary relation symbol ∈ ⓘ |
| hasUndecidableStatement |
axiom of choice
ⓘ
continuum hypothesis ⓘ generalized continuum hypothesis ⓘ |
| isExtendedBy |
ZFC
ⓘ
linked to:
ZF
|
| isFormalizedIn |
Hilbert-style deductive systems
ⓘ
natural deduction systems ⓘ |
| isIncompletenessSubjectTo |
Gödel incompleteness theorems
ⓘ
linked to:
Gödel's incompleteness theorems
|
| isStandardFrameworkFor | axiomatic set theory in mainstream mathematics ⓘ |
| language | first-order logic with equality ⓘ |
| namedAfter |
Abraham Fraenkel
ⓘ
Ernst Zermelo ⓘ |
| omitsAxiom | axiom of choice ⓘ |
| standardIn | foundations of mathematics ⓘ |
| underpins | much of modern mathematics ⓘ |
| usedFor |
foundations of algebra
ⓘ
foundations of analysis ⓘ foundations of topology ⓘ |
How these facts were elicited
The pipeline generated the facts above by prompting gpt-5.1 with this entity's name + description and the instruction below.
Instruction
You are a knowledge base construction expert. Given a subject entity and a description of it, return factual statements that you know for the subject as a JSON list of dictionaries(triples), where keys must be "subject", "predicate" and "object". The number of facts may be very high, between 25 to 50 or more, for very popular subjects. For less popular subjects, the number of facts can be very low, like 5 or 10. # Requirements - If you don't know the subject at all, return an empty list. - If the subject is not a named entity, return an empty list. - Include at least one triple where predicate is "instanceOf". - Do not get too wordy. - Separate several objects into multiple triples with one object.
Input
Subject: ZF Description of subject: ZF is the standard axiomatic framework for set theory that underpins much of modern mathematics.
Referenced by (10)
Full triples — surface form annotated when it differs from this entity's canonical label.
linked to: ZF
linked to: ZF
linked to: ZF
linked to: ZF
linked to: ZF
linked to: ZF
linked to: ZF
linked to: ZF
linked to: ZF