Category
page 1Large cardinals
large cardinal
cardinal number in set theory not provable from ZFC
inaccessible cardinal
cardinal unobtainable from smaller cardinals via usual cardinal arithmetic
Grothendieck universe
transitive set closed under the operations of parameterized union, power set and unordered pairs
measurable cardinal
large cardinal number that is the critical point of a nontrivial elementary embedding of the universe into a transitive class
axiom of determinacy
set-theoretic statement, consistent with ZF but contradicting choice, that any game corresponding to a subset of Baire space is determined
weakly compact cardinal
Mahlo cardinal 𝜅 such that every height‐𝜅 tree either has a size‐𝜅 level or a size‐𝜅 branch

Solovay model
set theory construction
Mahlo cardinal
inaccessible cardinal number 𝜅 such that the set of inaccessibles less than 𝜅 is stationary in 𝜅