Statements (56)
| Predicate | Object |
|---|---|
| gptkbp:instance_of |
gptkb:concept
|
| gptkbp:bfsLayer |
8
|
| gptkbp:bfsParent |
gptkb:Large_Cardinals
|
| gptkbp:are |
Considered by some as necessary for a complete understanding of set theory
A key concept in the study of set-theoretic hierarchies A topic in the study of the foundations of mathematics A subject of historical significance in the development of set theory A key area in the exploration of mathematical infinity A basis for many results in set-theoretic topology A framework for discussing the nature of infinity A part of the landscape of modern mathematics A part of the study of higher infinities A part of the study of mathematical infinity A source of many mathematical paradoxes A source of many open questions in mathematics A subject of debate among mathematicians A subject of interest in the study of model theory A subject of ongoing mathematical inquiry A subject of ongoing mathematical research A subject of research in set theory A topic in advanced mathematical logic A topic in the philosophy of mathematics A topic in the study of mathematical foundations A topic in the study of mathematical structures A topic in the study of ordinal numbers A topic of interest in the philosophy of infinity A key concept in the study of infinite combinatorics Connected to the concept of forcing Considered by some as axioms of infinity Used to prove the consistency of various mathematical statements A topic in the study of mathematical logic and set theory. Related to the concept of large sets Stronger than ZFC Used in the analysis of the continuum hypothesis A subject of interest in the study of mathematical logic A framework for understanding the nature of mathematical infinity A topic in the exploration of mathematical structures A source of inspiration for new mathematical theories A framework for discussing the nature of mathematical existence A subject of interest in the study of mathematical reasoning A framework for understanding the hierarchy of infinities A focus of research in the field of mathematical philosophy A subject of interest in the study of axiomatic systems A part of the discourse on the nature of mathematical truth Used to explore the limits of provability in mathematics A key area in the study of mathematical foundations |
| gptkbp:can_lead_to |
New axioms in set theory
|
| gptkbp:has_impact_on |
Consistency of mathematical theories
|
| https://www.w3.org/2000/01/rdf-schema#label |
Large cardinal axioms
|
| gptkbp:includes |
gptkb:Woodin_cardinals
Inaccessible cardinals Measurable cardinals |
| gptkbp:influence |
Foundations of mathematics
|
| gptkbp:proposed_by |
Large cardinals
|
| gptkbp:related_to |
Set theory
|
| gptkbp:used_in |
Mathematical logic
|