Statements (66)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:set_theory
|
| gptkbp:abbreviation |
gptkb:ZFC
|
| gptkbp:field |
gptkb:mathematics
gptkb:set_theory |
| gptkbp:formedBy |
early 20th century
|
| gptkbp:fullName |
gptkb:Zermelo–Fraenkel_set_theory_with_the_axiom_of_choice
|
| gptkbp:hasAxiom |
gptkb:axiom_schema_of_replacement
gptkb:axiom_of_empty_set gptkb:axiom_of_extensionality gptkb:axiom_of_pairing gptkb:axiom_of_power_set gptkb:axiom_of_regularity gptkb:axiom_of_union gptkb:axiom_schema_of_separation axiom of choice axiom of infinity |
| https://www.w3.org/2000/01/rdf-schema#label |
ZFC (with axiom of choice)
|
| gptkbp:isConsistentWith |
axiom of choice
|
| gptkbp:isFoundationFor |
modern set theory
much of mathematics |
| gptkbp:isStandardFormulationOf |
gptkb:set_theory
|
| gptkbp:isUndecidableIn |
gptkb:Banach–Tarski_paradox
gptkb:continuum_hypothesis gptkb:large_cardinal_axioms gptkb:Whitehead_problem gptkb:Suslin's_hypothesis axiom of constructibility existence of a nonprincipal ultrafilter on the natural numbers existence of a nontrivial elementary embedding of the universe existence of 0# (zero sharp) existence of a 0# (zero sharp) existence of a Lebesgue non-measurable set existence of a Mahlo cardinal existence of a Ramsey cardinal existence of a Reinhardt cardinal existence of a Woodin cardinal existence of a basis for every vector space existence of a huge cardinal existence of a measurable cardinal existence of a non-measurable set of reals existence of a strongly compact cardinal existence of a strongly inaccessible cardinal existence of a supercompact cardinal existence of a weakly compact cardinal existence of a well-ordering of the reals existence of inaccessible cardinals existence of inner models with large cardinals existence of measurable cardinals existence of a Hamel basis for the real numbers as a vector space over the rationals existence of nontrivial elementary embeddings of the universe |
| gptkbp:isWeakerThan |
gptkb:ZF_(Zermelo–Fraenkel_set_theory_without_choice)
|
| gptkbp:namedAfter |
gptkb:Ernst_Zermelo
gptkb:Abraham_Fraenkel |
| gptkbp:usedIn |
gptkb:algebra
gptkb:logic gptkb:topology gptkb:category_theory analysis foundations of mathematics model theory number theory proof theory combinatorics mathematical foundations |
| gptkbp:bfsParent |
gptkb:Zermelo–Fraenkel_axioms
|
| gptkbp:bfsLayer |
6
|