Statements (22)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
|
| gptkbp:appliesTo |
infinite sets
finite sets |
| gptkbp:field |
combinatorics
|
| gptkbp:generalizes |
gptkb:finite_Ramsey_theorem
|
| gptkbp:hasVersion |
gptkb:finite_Ramsey_theorem
gptkb:infinite_Ramsey_theorem |
| https://www.w3.org/2000/01/rdf-schema#label |
Ramsey's theorem for sets
|
| gptkbp:implies |
existence of homogeneous sets
|
| gptkbp:namedAfter |
gptkb:Frank_P._Ramsey
|
| gptkbp:publicationYear |
1930
|
| gptkbp:publishedIn |
gptkb:Proceedings_of_the_London_Mathematical_Society
|
| gptkbp:relatedTo |
gptkb:Ramsey_theory
|
| gptkbp:seeAlso |
gptkb:Ramsey_number
partition regularity |
| gptkbp:state |
For any coloring of the k-element subsets of an infinite set with finitely many colors, there exists an infinite subset all of whose k-element subsets have the same color.
|
| gptkbp:usedIn |
gptkb:logic
gptkb:set_theory theoretical computer science graph theory |
| gptkbp:bfsParent |
gptkb:Ramsey_theory
|
| gptkbp:bfsLayer |
5
|