mathematical field of set theory, a large cardinal property is a certain kind of property of transfinite cardinal numbers. Cardinals with such properties are, as...

In set theory, a strong cardinal is a type of large cardinal. It is a weakening of the notion of a supercompact cardinal. If λ is any ordinal, κ is λ-strong...

measurable cardinal is a certain kind of large cardinal number. In order to define the concept, one introduces a two-valued measure on a cardinal κ, or more...

This page includes a list of large cardinal properties in the mathematical field of set theory. It is arranged roughly in order of the consistency strength...

In set theory, a supercompact cardinal is a type of large cardinal independently introduced by Solovay and Reinhardt. They display a variety of reflection...

a cardinal number, or cardinal for short, is what is commonly called the number of elements of a set. In the case of a finite set, its cardinal number...

successors of singular cardinals. Write κ , λ {\displaystyle \kappa ,\lambda } for ordinals, m {\displaystyle m} for a cardinal number (finite or infinite)...

set theory, a cardinal number is a strongly inaccessible cardinal if it is uncountable, regular, and a strong limit cardinal. A cardinal is a weakly inaccessible...

Member of the College of Cardinals Cardinal Health, a health care services company Cardinal number Large cardinal Cardinal direction, one of the four...

In mathematics, subtle cardinals and ethereal cardinals are closely related kinds of large cardinal number. A cardinal κ {\displaystyle \kappa } is called...

structure of the real number line to the study of the consistency of large cardinals. The basic notion of grouping objects has existed since at least the...

In set theory, a Woodin cardinal (named for W. Hugh Woodin) is a cardinal number λ {\displaystyle \lambda } such that for all functions f : λ → λ {\displaystyle...

Mahlo cardinal is a certain kind of large cardinal number. Mahlo cardinals were first described by Paul Mahlo (1911, 1912, 1913). As with all large cardinals...

Weakly Mahlo cardinals become strongly Mahlo. And more generally, any large cardinal property weaker than 0# (see the list of large cardinal properties)...

attraction of large cardinal axioms is that they enable many results from ZF+AD to be established in ZFC adjoined by some large cardinal axiom. The Mizar...

cardinal, also called a partition cardinal is a certain kind of large cardinal number introduced by Paul Erdős and András Hajnal (1958). A cardinal κ...

extendible cardinals are large cardinals introduced by Reinhardt (1974), who was partly motivated by reflection principles. Intuitively, such a cardinal represents...

In mathematics, an unfoldable cardinal is a certain kind of large cardinal number. Formally, a cardinal number κ is λ-unfoldable if and only if for every...

mathematics, a remarkable cardinal is a certain kind of large cardinal number. A cardinal κ is called remarkable if for all regular cardinals θ > κ, there exist...

In set theory, a Reinhardt cardinal is a kind of large cardinal. Reinhardt cardinals are considered under ZF (Zermelo–Fraenkel set theory without the...

set theory, a Jónsson cardinal (named after Bjarni Jónsson) is a certain kind of large cardinal number. An uncountable cardinal number κ is said to be...

In mathematics, a cardinal number κ {\displaystyle \kappa } is called huge if there exists an elementary embedding j : V → M {\displaystyle j:V\to M} from...

In set theory, a strongly compact cardinal is a certain kind of large cardinal. An uncountable cardinal κ is strongly compact if and only if every κ-complete...

Cardinal function Inaccessible cardinal Infinitary combinatorics Large cardinal List of large cardinal properties Regular cardinal Scott's trick The Higher...

universe, with important methodological consequences. The absoluteness of large cardinal axioms is also studied, with positive and negative results known. In...

axioms for set theory, such as some axioms asserting existence of large cardinals. In trying to formalize the argument for the reflection principle of...

In mathematics, a Ramsey cardinal is a certain kind of large cardinal number introduced by Erdős & Hajnal (1962) and named after Frank P. Ramsey, whose...

In set theory, Berkeley cardinals are certain large cardinals suggested by Hugh Woodin in a seminar at the University of California, Berkeley in about...

weakly compact cardinal is a certain kind of cardinal number introduced by Erdős & Tarski (1961); weakly compact cardinals are large cardinals, meaning that...

theory, a Rowbottom cardinal, introduced by Rowbottom (1971), is a certain kind of large cardinal number. An uncountable cardinal number κ {\displaystyle...