Statements (50)
| Predicate | Object |
|---|---|
| gptkbp:instance_of |
gptkb:Cardinal
|
| gptkbp:bfsLayer |
6
|
| gptkbp:bfsParent |
gptkb:W._Hugh_Woodin
|
| gptkbp:are |
a subject of research in mathematical logic
a type of cardinal number strongly inaccessible related to set theory a subject of ongoing research in mathematical logic discussed in relation to the concept of determinacy in games a subject of interest in the study of the foundations of set theory a topic of interest for set theorists and logicians alike a significant concept in the landscape of modern logic often explored in the context of large cardinal axioms connected to the concept of large cardinals in set theory a focus of research in the foundations of mathematics a central topic in the study of large cardinals a part of the hierarchy of large cardinals a part of the landscape of modern set theory associated with the concept of inner models considered to be a strong form of infinity discussed in relation to the axiom of choice named after the mathematician Hugh Woodin often studied in the context of inner model theory related to the concept of reflection principles related to the study of definable sets stronger than measurable cardinals used in the study of determinacy used in the analysis of the structure of the set-theoretic universe a type of cardinal that extends the notion of measurable cardinals important for understanding the hierarchy of infinite sets a significant area of research in mathematical foundations. discussed in the context of forcing and independence results related to the study of the consistency of various mathematical theories a significant area of inquiry in mathematical logic a key concept in the study of set-theoretic forcing a part of the broader study of cardinal characteristics of the continuum a topic of interest in the philosophy of mathematics considered to be a significant topic in the field of set theory a key concept in the study of the continuum hypothesis |
| gptkbp:can_be |
be used to analyze the nature of mathematical truth
be used to investigate the nature of mathematical infinity be used to analyze the foundations of mathematics be used to construct models of set theory be used to explore the limits of provability in mathematics be characterized by certain combinatorial properties be used to prove the consistency of certain mathematical statements be used to derive results about other large cardinals |
| gptkbp:have |
properties that relate to the structure of the set-theoretic universe
|
| https://www.w3.org/2000/01/rdf-schema#label |
Woodin cardinals
|
| gptkbp:indication |
the existence of a proper class of measurable cardinals
|