Algebraic Set Theory
E777846
Algebraic Set Theory is a branch of mathematical logic that develops set theory within a categorical and algebraic framework, often using topos theory and related structures.
All labels observed (1)
| Label | Occurrences |
|---|---|
| Algebraic Set Theory canonical | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T9095778 — 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: Algebraic Set Theory Context triple: [Ieke Moerdijk, notableWork, Algebraic Set Theory]
-
A.
Lattice Theory
Lattice Theory is a foundational mathematical text that systematically develops the theory of lattices and ordered structures, profoundly influencing modern algebra and order theory.
-
B.
Universal Algebra
Universal Algebra is a foundational mathematical text that systematically studies algebraic structures in a unified, abstract framework.
-
C.
Grothendieck universe
A Grothendieck universe is a set-theoretic construct large enough to contain all the usual objects and operations of mathematics, used to rigorously handle "large" categories while avoiding paradoxes.
-
D.
set theory
Set theory is a foundational branch of mathematical logic that studies collections of objects, called sets, and underpins much of modern mathematics.
-
E.
Kripke–Platek set theory
Kripke–Platek set theory is a weaker, predicative subsystem of Zermelo–Fraenkel set theory focused on sets that are explicitly constructible and often used in the study of admissible sets and recursion theory.
- 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: Algebraic Set Theory Target entity description: Algebraic Set Theory is a branch of mathematical logic that develops set theory within a categorical and algebraic framework, often using topos theory and related structures.
-
A.
Lattice Theory
Lattice Theory is a foundational mathematical text that systematically develops the theory of lattices and ordered structures, profoundly influencing modern algebra and order theory.
-
B.
Universal Algebra
Universal Algebra is a foundational mathematical text that systematically studies algebraic structures in a unified, abstract framework.
-
C.
Grothendieck universe
A Grothendieck universe is a set-theoretic construct large enough to contain all the usual objects and operations of mathematics, used to rigorously handle "large" categories while avoiding paradoxes.
-
D.
set theory
Set theory is a foundational branch of mathematical logic that studies collections of objects, called sets, and underpins much of modern mathematics.
-
E.
Kripke–Platek set theory
Kripke–Platek set theory is a weaker, predicative subsystem of Zermelo–Fraenkel set theory focused on sets that are explicitly constructible and often used in the study of admissible sets and recursion theory.
- F. None of above. chosen
Statements (47)
| Predicate | Object |
|---|---|
| instanceOf |
branch of mathematical logic
ⓘ
research area ⓘ |
| aimsTo |
axiomatize set-theoretic universes categorically
ⓘ
develop set theory in a categorical framework ⓘ |
| allows | interpretation of set-theoretic axioms in categories ⓘ |
| analyzes |
axioms of collection
ⓘ
axioms of replacement ⓘ axioms of separation ⓘ power set principles ⓘ |
| connects |
large cardinal principles with categorical structure
ⓘ
set-theoretic universes with categorical universes ⓘ |
| contrastsWith | classical axiomatic set theory in first-order logic ⓘ |
| developedIn |
early 21st century
ⓘ
late 20th century ⓘ |
| emphasizes |
functorial and categorical constructions
ⓘ
structural properties of sets and classes ⓘ |
| fieldOfStudy |
category theory
ⓘ
set theory ⓘ topos theory ⓘ |
| formalizes | set-theoretic notions in categorical language ⓘ |
| generalizes | topos-theoretic interpretations of set theory ⓘ |
| hasApplicationIn |
categorical logic
ⓘ
constructive mathematics ⓘ foundations of mathematics ⓘ type theory ⓘ |
| isBasedOn |
category of classes
ⓘ
category of sets ⓘ small maps axioms ⓘ |
| isRelatedTo |
constructive Zermelo–Fraenkel set theory
NERFINISHED
ⓘ
internal set theory of a topos ⓘ intuitionistic set theory ⓘ predicative algebraic set theories ⓘ topos-theoretic foundations of mathematics ⓘ |
| isSubfieldOf |
foundations of set theory
ⓘ
mathematical logic ⓘ |
| oftenUses |
intuitionistic logic
ⓘ
predicative reasoning ⓘ |
| provides |
categorical semantics for set theories
ⓘ
models of set theory in categories ⓘ |
| studies |
categories with class-like structure
ⓘ
categories with small maps ⓘ constructive set theories ⓘ predicative set theories ⓘ relations between set theories and toposes ⓘ |
| uses |
algebraic methods
ⓘ
categorical methods ⓘ topos-theoretic techniques ⓘ |
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: Algebraic Set Theory Description of subject: Algebraic Set Theory is a branch of mathematical logic that develops set theory within a categorical and algebraic framework, often using topos theory and related structures.
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.