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.
All labels observed (1)
| Label | Occurrences |
|---|---|
| Isabelle/ZF canonical | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T9810053 — 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: Isabelle/ZF Context triple: [Isabelle, hasComponent, Isabelle/ZF]
-
A.
Isabelle/FOL
Isabelle/FOL is the classical first-order logic object logic of the Isabelle proof assistant, providing a framework for formalizing and verifying mathematical theorems and logical systems.
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B.
Isabelle proof assistant
Isabelle proof assistant is a widely used interactive theorem prover and generic proof assistant designed for formal verification and mathematical logic, particularly known for its support of higher-order logic.
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C.
Isabelle/ML
Isabelle/ML is the ML-based implementation and extension language used to develop and script the Isabelle interactive theorem prover.
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D.
Isabelle/Isar Reference Manual
The Isabelle/Isar Reference Manual is the official technical guide detailing the structured proof language Isar used within the Isabelle interactive theorem prover.
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E.
Isabelle/HOL: A Proof Assistant for Higher-Order Logic
"Isabelle/HOL: A Proof Assistant for Higher-Order Logic" is a foundational book and system documentation that presents the Isabelle/HOL interactive theorem prover, widely used for formal verification and higher-order logic reasoning in computer science and mathematics.
- 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: Isabelle/ZF Target entity description: Isabelle/ZF is a formalization of Zermelo–Fraenkel set theory within the Isabelle proof assistant, providing a foundational framework for developing and verifying mathematics.
-
A.
Isabelle/FOL
Isabelle/FOL is the classical first-order logic object logic of the Isabelle proof assistant, providing a framework for formalizing and verifying mathematical theorems and logical systems.
-
B.
Isabelle proof assistant
Isabelle proof assistant is a widely used interactive theorem prover and generic proof assistant designed for formal verification and mathematical logic, particularly known for its support of higher-order logic.
-
C.
Isabelle/ML
Isabelle/ML is the ML-based implementation and extension language used to develop and script the Isabelle interactive theorem prover.
-
D.
Isabelle/Isar Reference Manual
The Isabelle/Isar Reference Manual is the official technical guide detailing the structured proof language Isar used within the Isabelle interactive theorem prover.
-
E.
Isabelle/HOL: A Proof Assistant for Higher-Order Logic
"Isabelle/HOL: A Proof Assistant for Higher-Order Logic" is a foundational book and system documentation that presents the Isabelle/HOL interactive theorem prover, widely used for formal verification and higher-order logic reasoning in computer science and mathematics.
- F. None of above. chosen
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 ⓘ |
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: Isabelle/ZF Description of subject: Isabelle/ZF is a formalization of Zermelo–Fraenkel set theory within the Isabelle proof assistant, providing a foundational framework for developing and verifying mathematics.
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.
subject surface form:
Isabelle