Hilbert's first problem

E628900

Hilbert's first problem is one of David Hilbert’s famous list of 23 problems, asking whether there exists a set whose size is strictly between that of the integers and the real numbers, i.e., the status of the continuum hypothesis.

All labels observed (1)

Label Occurrences
Hilbert's first problem canonical 1

How this entity was disambiguated

Statements (44)

Predicate Object
instanceOf mathematical problem ⓘ
asksWhether there exists a set of cardinality strictly between the integers and the real numbers ⓘ
there exists a set whose cardinality is strictly between aleph-null and the cardinality of the continuum ⓘ
concerns cardinality of infinite sets ⓘ
continuum hypothesis ⓘ
foundations of mathematics ⓘ
set theory ⓘ
equivalentToQuestion Is the continuum hypothesis true? ⓘ
firstPublishedIn 1900 ⓘ
formalContext Zermelo–Fraenkel set theory ⓘ
Zermelo–Fraenkel set theory with Choice ⓘ
hasPhilosophicalAspect completeness of axiomatic systems ⓘ
nature of mathematical infinity ⓘ
hasSolutionType independence result ⓘ
hasStandardFormulation Is there a set whose cardinality is strictly between that of the integers and that of the real numbers? ⓘ
influencedField foundations of mathematics ⓘ
mathematical logic ⓘ
set theory ⓘ
involvesConcept aleph-null ⓘ
cardinality of the continuum ⓘ
integers ⓘ
real numbers ⓘ
set-theoretic independence ⓘ
uncountable sets ⓘ
languageOfOriginalStatement German ⓘ
namedAfter David Hilbert ⓘ
numberInHilbertList 1 ⓘ
originalPublication Mathematische Probleme (Hilbert's 1900 address) ⓘ
linked to: Hilbert problems
partOf Hilbert's list of 23 problems ⓘ
linked to: Hilbert problems
presentedAt International Congress of Mathematicians 1900 ⓘ
presentedInCity Paris ⓘ
relatedTo Cantor's continuum hypothesis ⓘ
generalized continuum hypothesis ⓘ
resolutionYearPartial 1938 ⓘ
resolutionYearPartial 1940 ⓘ
1963 ⓘ
resolvedBy Kurt Gödel ⓘ
Paul Cohen ⓘ
resultByCohen continuum hypothesis is independent of ZF if ZF is consistent ⓘ
continuum hypothesis is independent of ZFC if ZFC is consistent ⓘ
resultByGödel continuum hypothesis is consistent with ZF if ZF is consistent ⓘ
resultByGödel continuum hypothesis is consistent with ZFC if ZFC is consistent ⓘ
statedBy David Hilbert ⓘ
statusInZFC independent ⓘ

How these facts were elicited

Referenced by (1)

Full triples — surface form annotated when it differs from this entity's canonical label.

continuum hypothesis → positionInHilbertProblems → Hilbert's first problem ⓘ