Grundzüge der Mengenlehre
E608813
Grundzüge der Mengenlehre is a foundational early 20th-century textbook on set theory that helped formalize and shape modern axiomatic set theory and topology.
All labels observed (2)
| Label | Occurrences |
|---|---|
| Grundzüge der Mengenlehre canonical | 1 |
| Set Theory (English translation of Grundzüge der Mengenlehre) | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T6660367 — 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: Grundzüge der Mengenlehre Context triple: [Felix Hausdorff, notableWork, Grundzüge der Mengenlehre]
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A.
Einleitung in die Mengenlehre
Einleitung in die Mengenlehre is a foundational textbook on set theory authored by mathematician Abraham Fraenkel, which helped shape the modern axiomatic treatment of sets.
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B.
Untersuchungen über die Grundlagen der Mengenlehre
Untersuchungen über die Grundlagen der Mengenlehre is Ernst Zermelo’s foundational work in set theory, in which he formulated and axiomatized key principles that shaped modern axiomatic set theory.
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C.
Grundgesetze der Arithmetik, Volume I
Grundgesetze der Arithmetik, Volume I is Gottlob Frege’s foundational work in logic and the philosophy of mathematics, in which he develops his formal system aimed at deriving arithmetic from purely logical principles.
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D.
Grundgesetze der Arithmetik, Volume II
Grundgesetze der Arithmetik, Volume II is the second volume of Gottlob Frege’s foundational work in logic and the philosophy of mathematics, in which he further develops and applies his formal system for arithmetic.
-
E.
Foundations of Set Theory (with Andrey Kolmogorov)
"Foundations of Set Theory" is a classic 20th-century mathematical text co-authored by Pavel Alexandrov and Andrey Kolmogorov that systematically develops the basic concepts and axioms of set 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: Grundzüge der Mengenlehre Target entity description: Grundzüge der Mengenlehre is a foundational early 20th-century textbook on set theory that helped formalize and shape modern axiomatic set theory and topology.
-
A.
Einleitung in die Mengenlehre
Einleitung in die Mengenlehre is a foundational textbook on set theory authored by mathematician Abraham Fraenkel, which helped shape the modern axiomatic treatment of sets.
-
B.
Untersuchungen über die Grundlagen der Mengenlehre
Untersuchungen über die Grundlagen der Mengenlehre is Ernst Zermelo’s foundational work in set theory, in which he formulated and axiomatized key principles that shaped modern axiomatic set theory.
-
C.
Grundgesetze der Arithmetik, Volume I
Grundgesetze der Arithmetik, Volume I is Gottlob Frege’s foundational work in logic and the philosophy of mathematics, in which he develops his formal system aimed at deriving arithmetic from purely logical principles.
-
D.
Grundgesetze der Arithmetik, Volume II
Grundgesetze der Arithmetik, Volume II is the second volume of Gottlob Frege’s foundational work in logic and the philosophy of mathematics, in which he further develops and applies his formal system for arithmetic.
-
E.
Foundations of Set Theory (with Andrey Kolmogorov)
"Foundations of Set Theory" is a classic 20th-century mathematical text co-authored by Pavel Alexandrov and Andrey Kolmogorov that systematically develops the basic concepts and axioms of set theory.
- F. None of above. chosen
Statements (43)
| Predicate | Object |
|---|---|
| instanceOf |
book
ⓘ
mathematics textbook ⓘ set theory textbook ⓘ |
| author | Felix Hausdorff NERFINISHED ⓘ |
| authorNameString | Felix Hausdorff NERFINISHED ⓘ |
| citedBy |
later textbooks on set theory
ⓘ
research papers in topology ⓘ |
| classification |
set theory literature
ⓘ
topology literature ⓘ |
| contributedTo |
development of axiomatic set theory
ⓘ
development of general topology ⓘ |
| countryOfOrigin | Germany ⓘ |
| field |
foundations of mathematics
ⓘ
set theory ⓘ topology ⓘ |
| genre |
mathematics monograph
ⓘ
scientific literature ⓘ |
| hasAuthor | Felix Hausdorff NERFINISHED ⓘ |
| hasInfluenceOn |
20th-century foundational studies in mathematics
ⓘ
Bourbaki's set-theoretic approach ⓘ |
| historicalPeriod | early 20th century ⓘ |
| impact |
helped formalize modern axiomatic set theory
ⓘ
helped shape modern topology ⓘ |
| influenced |
mathematical logic
ⓘ
modern set theory ⓘ modern topology ⓘ |
| inSeries | Hausdorff's works on set theory and topology ⓘ |
| isEarlyWorkIn |
axiomatic set theory
ⓘ
general topology ⓘ |
| notableFor |
early axiomatic approach to set theory
ⓘ
introduction of topological ideas ⓘ systematic treatment of set-theoretic concepts ⓘ |
| originalLanguage | German ⓘ |
| publicationYear | 1914 ⓘ |
| publisher | Veit & Comp. NERFINISHED ⓘ |
| subject |
cardinal numbers
ⓘ
infinite sets ⓘ order types ⓘ ordinal numbers ⓘ point-set topology ⓘ |
| title | Grundzüge der Mengenlehre ⓘ |
| titleTranslation | Foundations of Set Theory NERFINISHED ⓘ |
| usedIn | advanced mathematics education ⓘ |
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: Grundzüge der Mengenlehre Description of subject: Grundzüge der Mengenlehre is a foundational early 20th-century textbook on set theory that helped formalize and shape modern axiomatic set theory and topology.
Referenced by (2)
Full triples — surface form annotated when it differs from this entity's canonical label.
this entity surface form:
Set Theory (English translation of Grundzüge der Mengenlehre)