Statements (51)
| Predicate | Object |
|---|---|
| gptkbp:instance_of |
gptkb:Cardinal
|
| gptkbp:bfsLayer |
8
|
| gptkbp:bfsParent |
gptkb:Large_Cardinals
|
| gptkbp:contains |
inner models
|
| gptkbp:has_ability |
measurable cardinal
supercompact cardinal |
| gptkbp:has_property |
being a limit of cardinals
|
| https://www.w3.org/2000/01/rdf-schema#label |
Woodin cardinal
|
| gptkbp:is_aligned_with |
ZFC axioms
|
| gptkbp:is_associated_with |
large cardinal hierarchy
|
| gptkbp:is_related_to |
gptkb:collection
determinacy |
| gptkbp:is_studied_in |
large cardinals
mathematical logic |
| gptkbp:is_tested_for |
the consistency of certain theories
|
| gptkbp:is_used_in |
forcing
|
| gptkbp:key |
set-theoretic foundations
|
| gptkbp:named_after |
W. H. Woodin
|
| gptkbp:papal_bull |
a central topic in the field of mathematical logic.
used to explore the implications of large cardinals a focus of ongoing research in logic and set theory a certain level of strength a focus of research in mathematical logic a part of the study of higher infinities a significant concept in modern set theory a subject of debate among mathematicians considered in the context of set-theoretic axioms important in the context of determinacy larger than any countable cardinal measured by certain properties not necessarily measurable related to the concept of reflection the Woodin condition used in combinatorial set theory used in the study of large cardinals used to analyze the properties of sets used to analyze the structure of sets used to construct models used to derive certain mathematical results used to explore the foundations of mathematics used to investigate the nature of infinity used to study the continuum hypothesis used to understand the limits of set theory used to investigate the nature of mathematical truth a key element in the study of set-theoretic hierarchies used to study the relationships between different types of cardinals a topic of interest in the philosophy of mathematics |
| gptkbp:related_concept |
gptkb:collection
|
| gptkbp:type_of |
gptkb:Cardinal
large cardinal axiom strongly inaccessible cardinal |