Foundations of Set Theory (with Andrey Kolmogorov)
E173183
"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.
All labels observed (2)
| Label | Occurrences |
|---|---|
| Foundations of Set Theory | 1 |
| Foundations of Set Theory (with Andrey Kolmogorov) canonical | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T1509459 — 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.
Target entity: Foundations of Set Theory (with Andrey Kolmogorov) Context triple: [Pavel Alexandrov, notableWork, Foundations of Set Theory (with Andrey Kolmogorov)]
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A.
Remarks on the Foundations of Mathematics
Remarks on the Foundations of Mathematics is a posthumously published collection of Ludwig Wittgenstein’s later writings that critically examines the nature of mathematical truth, proof, and practice from a philosophical and language-centered perspective.
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B.
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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C.
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.
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D.
Morse–Kelley set theory by class–set distinction
Morse–Kelley set theory by class–set distinction is a foundational system that avoids certain set-theoretic paradoxes by rigorously distinguishing between sets and proper classes within a powerful axiomatic framework.
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E.
Ulam problem in set theory
The Ulam problem in set theory is a well-known question posed by Stanislaw Ulam concerning the structure and properties of measurable sets and functions, particularly in relation to homomorphisms and measure-theoretic regularity.
- F. None of above. chosen
- G. Unsure - the case is ambiguous/there is not enough information to decide.
Target entity: Foundations of Set Theory (with Andrey Kolmogorov) Target entity description: "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.
-
A.
Remarks on the Foundations of Mathematics
Remarks on the Foundations of Mathematics is a posthumously published collection of Ludwig Wittgenstein’s later writings that critically examines the nature of mathematical truth, proof, and practice from a philosophical and language-centered perspective.
-
B.
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.
-
C.
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.
-
D.
Morse–Kelley set theory by class–set distinction
Morse–Kelley set theory by class–set distinction is a foundational system that avoids certain set-theoretic paradoxes by rigorously distinguishing between sets and proper classes within a powerful axiomatic framework.
-
E.
Ulam problem in set theory
The Ulam problem in set theory is a well-known question posed by Stanislaw Ulam concerning the structure and properties of measurable sets and functions, particularly in relation to homomorphisms and measure-theoretic regularity.
- F. None of above. chosen
Statements (40)
| Predicate | Object |
|---|---|
| instanceOf |
mathematics book
ⓘ
set theory book ⓘ textbook ⓘ |
| aim | systematic development of basic set-theoretic concepts ⓘ |
| approach | axiomatic method ⓘ |
| associatedWith |
Moscow school of mathematics
ⓘ
surface form:
Moscow mathematical school
|
| author |
Andrei Kolmogorov
ⓘ
surface form:
Andrey Kolmogorov
Pavel Alexandrov ⓘ |
| coAuthorWith |
Andrei Kolmogorov
ⓘ
surface form:
Andrey Kolmogorov
Pavel Alexandrov ⓘ |
| countryOfOrigin | Soviet Union ⓘ |
| covers |
Zermelo–Fraenkel-style axioms of set theory
ⓘ
operations on sets ⓘ set-theoretic constructions used in analysis ⓘ |
| educationalUse | introduction to modern set theory ⓘ |
| field |
mathematical logic
ⓘ
set theory ⓘ |
| genre | mathematics textbook ⓘ |
| hasForm | printed book ⓘ |
| hasInfluenceOn | Soviet-era curricula in analysis and topology ⓘ |
| influencedBy | early 20th-century axiomatic set theory ⓘ |
| intendedAudience |
students of mathematics
ⓘ
teachers of mathematics ⓘ |
| language | Russian ⓘ |
| notableFor |
clear exposition of elementary set theory
ⓘ
influence on teaching of set theory in the Soviet Union ⓘ |
| originalTitle | Основы теории множеств ⓘ |
| pedagogicalLevel |
beginning graduate
ⓘ
undergraduate ⓘ |
| publicationCentury | 20th century ⓘ |
| structure | systematic, axiomatic presentation ⓘ |
| topic |
axiomatic set theory
ⓘ
basic concepts of set theory ⓘ cardinal numbers ⓘ cardinality ⓘ infinite sets ⓘ ordinal numbers ⓘ relations and functions ⓘ sets and subsets ⓘ |
| usedAs | university textbook ⓘ |
How these facts were elicited
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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.
Subject: Foundations of Set Theory (with Andrey Kolmogorov) Description of subject: "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.
Referenced by (2)
Full triples — surface form annotated when it differs from this entity's canonical label.