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 |
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 ⓘ |
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.