Statements (55)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:Titan
|
| gptkbp:category |
gptkb:Axiom_schema
Mathematical axiom Set-theoretic axiom |
| gptkbp:consistencyStrength |
Stronger than ZFC
|
| gptkbp:describes |
Properties of large cardinals
|
| gptkbp:example |
0# (Zero Sharp)
Erdős Cardinals Extendible Cardinals Huge Cardinals Inaccessible Cardinals Indescribable Cardinals Ineffable Cardinals Mahlo Cardinals Measurable Cardinals Ramsey Cardinals Reflecting Cardinals Strong Cardinals Strongly Compact Cardinals Subtle Cardinals Supercompact Cardinals Superstrong Cardinals Weakly Compact Cardinals Woodin Cardinals |
| gptkbp:field |
gptkb:Set_Theory
|
| gptkbp:hasHierarchy |
Ordered by consistency strength
|
| https://www.w3.org/2000/01/rdf-schema#label |
Large Cardinal Axioms
|
| gptkbp:implies |
Existence of large cardinals
|
| gptkbp:influenced |
gptkb:Continuum_Hypothesis
gptkb:Descriptive_Set_Theory Determinacy Axioms Forcing Axioms Inner Model Theory |
| gptkbp:introducedIn |
20th Century
|
| gptkbp:motive |
Exploring independence results
Study of infinite hierarchies Understanding consistency strength |
| gptkbp:notablePerson |
gptkb:Dana_Scott
gptkb:Kurt_Gödel gptkb:Paul_Cohen gptkb:William_Mitchell gptkb:John_Steel gptkb:W._Hugh_Woodin gptkb:Matthew_Foreman gptkb:Kenneth_Kunen gptkb:Jindřich_Zapletal gptkb:Menachem_Magidor gptkb:Ronald_Jensen Hugh Woodin |
| gptkbp:notProvableIn |
gptkb:ZFC
|
| gptkbp:relatedTo |
gptkb:logic
|
| gptkbp:usedIn |
Foundations of Mathematics
|
| gptkbp:bfsParent |
gptkb:Projective_Determinacy
gptkb:ZFC_(Zermelo–Fraenkel_set_theory_with_Choice) |
| gptkbp:bfsLayer |
8
|