3 articles
Inaccessible cardinal
An inaccessible cardinal is an uncountable cardinal that cannot be reached from smaller cardinals by successor, union, and power set operations, and whose existence ZFC cannot prove.
Indescribable cardinal
An indescribable cardinal is a large cardinal whose higher-order statements about Vκ already hold in some smaller Vα, introduced by Hanf and Scott in 1961.
Mahlo cardinal
A Mahlo cardinal, also called a strongly Mahlo cardinal, is a large cardinal that is inaccessible and a stationary limit of regular cardinals, introduced by Paul Mahlo in 1911.