Einleitung in die Mengenlehre
E399415
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.
All labels observed (1)
| Label | Occurrences |
|---|---|
| Einleitung in die Mengenlehre canonical | 2 |
How this entity was disambiguated
This entity first appeared as the object of triple T3931000 — 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: Einleitung in die Mengenlehre Context triple: [Abraham Fraenkel, notableWork, Einleitung in die Mengenlehre]
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A.
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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B.
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.
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C.
Zermelo set theory
Zermelo set theory is an early axiomatic system for set theory, introduced by Ernst Zermelo to rigorously formalize the concept of sets and avoid known paradoxes.
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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.
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E.
Zermelo–Fraenkel set theory
Zermelo–Fraenkel set theory is the standard axiomatic framework for modern set theory, designed to avoid paradoxes and provide a rigorous foundation for much of 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: Einleitung in die Mengenlehre Target entity description: 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.
-
A.
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.
-
B.
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.
-
C.
Zermelo set theory
Zermelo set theory is an early axiomatic system for set theory, introduced by Ernst Zermelo to rigorously formalize the concept of sets and avoid known paradoxes.
-
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.
Zermelo–Fraenkel set theory
Zermelo–Fraenkel set theory is the standard axiomatic framework for modern set theory, designed to avoid paradoxes and provide a rigorous foundation for much of mathematics.
- F. None of above. chosen
Statements (30)
| Predicate | Object |
|---|---|
| instanceOf |
mathematics book
ⓘ
set theory book ⓘ textbook ⓘ |
| author | Abraham Fraenkel ⓘ |
| contributedTo |
modern treatment of sets
ⓘ
standardization of axiomatic set theory ⓘ |
| countryOfOrigin | Germany ⓘ |
| field | set theory ⓘ |
| genre | academic textbook ⓘ |
| hasAuthorRole | Abraham Fraenkel ⓘ |
| hasSubject |
Zermelo–Fraenkel set theory
ⓘ
axiomatic set theory ⓘ axioms of set theory ⓘ cardinal numbers ⓘ cardinality of sets ⓘ choice principle ⓘ infinite sets ⓘ naive set theory ⓘ ordinal numbers ⓘ set-theoretic paradoxes ⓘ well-ordering principle ⓘ |
| influenced |
axiomatic set theory
ⓘ
foundations of mathematics ⓘ |
| intendedAudience |
mathematicians
ⓘ
university students ⓘ |
| language | German ⓘ |
| notableFor |
influence on 20th-century set theory
ⓘ
systematic exposition of set-theoretic axioms ⓘ |
| topic |
foundations of mathematics
ⓘ
mathematical logic ⓘ |
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: Einleitung in die Mengenlehre Description of subject: 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.
Referenced by (2)
Full triples — surface form annotated when it differs from this entity's canonical label.
subject surface form:
Abraham Fraenkel