Isabelle/ZF
E824318
Isabelle/ZF is a formalization of Zermelo–Fraenkel set theory within the Isabelle proof assistant, providing a foundational framework for developing and verifying mathematics.
Statements (46)
| Predicate | Object |
|---|---|
| instanceOf |
Isabelle object logic
ⓘ
formalization of set theory ⓘ foundational framework for mathematics ⓘ |
| basedOn | Zermelo–Fraenkel set theory NERFINISHED ⓘ |
| developedAt | Technische Universität München NERFINISHED ⓘ |
| hasFeature |
integration with Isabelle automation tools
ⓘ
library of standard set-theoretic results ⓘ shallow embedding of ZF in Isabelle ⓘ support for definitional extensions ⓘ support for locales and structured theories ⓘ support for theory imports and modular development ⓘ |
| implementedIn | Isabelle NERFINISHED ⓘ |
| license | open-source license (Isabelle license) ⓘ |
| logicStyle | classical higher-order logic with sets as objects ⓘ |
| maintainedWith | Isabelle distribution ⓘ |
| partOf | Isabelle proof assistant NERFINISHED ⓘ |
| provides |
axiom of choice (optional)
ⓘ
axiom of extensionality ⓘ axiom of foundation ⓘ axiom of infinity ⓘ axiom of pairing ⓘ axiom of union ⓘ axiom schema of replacement ⓘ axiom schema of separation ⓘ axioms of Zermelo–Fraenkel set theory ⓘ definitions of cardinals ⓘ definitions of functions as sets of pairs ⓘ definitions of natural numbers ⓘ definitions of ordered pairs ⓘ definitions of ordinals ⓘ definitions of relations ⓘ induction principles on natural numbers ⓘ recursion principles on natural numbers ⓘ theory of arithmetic in set-theoretic encoding ⓘ theory of cardinals and cardinal arithmetic ⓘ theory of finite sets ⓘ theory of ordinals and ordinal arithmetic ⓘ theory of rank hierarchy ⓘ theory of transitive sets ⓘ theory of well-founded relations ⓘ |
| supports |
formal verification of mathematics
ⓘ
machine-checked proofs ⓘ |
| usedFor |
developing formalized mathematics
ⓘ
meta-theoretical studies of set theory ⓘ teaching formal methods in set theory ⓘ verifying set-theoretic constructions ⓘ |
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.
subject surface form:
Isabelle