Statements (31)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:set_theory
|
| gptkbp:basedOn |
Zermelo-Fraenkel set theory with Choice
|
| gptkbp:consistencyStrength |
greater than ZFC
|
| gptkbp:extendsTo |
gptkb:ZFC
|
| gptkbp:hasAxiom |
gptkb:large_cardinal_axiom
|
| gptkbp:hasOpenProblems |
consistency of large cardinal axioms
relationship to determinacy axioms |
| https://www.w3.org/2000/01/rdf-schema#label |
ZFC with large cardinals
|
| gptkbp:implies |
ZFC is consistent if ZFC with large cardinals is consistent
|
| gptkbp:notProvableIn |
gptkb:ZFC
|
| gptkbp:relatedTo |
supercompact cardinals
0# (zero sharp) Ramsey cardinals Woodin cardinals inaccessible cardinals indescribable cardinals measurable cardinals strong cardinals |
| gptkbp:studiedBy |
gptkb:projective_determinacy
gptkb:descriptive_set_theory forcing set theorists inner model theory relative consistency |
| gptkbp:usedFor |
independence proofs
consistency results |
| gptkbp:usedIn |
gptkb:logic
foundations of mathematics |
| gptkbp:bfsParent |
gptkb:Kelley–Morse_set_theory
gptkb:Morse–Kelley_class_theory |
| gptkbp:bfsLayer |
7
|