a regular cardinal is a cardinal number that is equal to its own cofinality. More explicitly, this means that κ {\displaystyle \kappa } is a regular cardinal...

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...

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...

sets Partition regularity Regular cardinal, a cardinal number that is equal to its cofinality Regular modal logic Regular conditional probability, a...

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...

operators are allowed to take infinitely many operands. The logic on a regular cardinal κ is defined by requiring the number of operands for each operator...

Mahlo cardinal", though the cardinals originally considered by Mahlo were weakly Mahlo cardinals. If κ is a limit ordinal and the set of regular ordinals...

interval of regular cardinals (i.e., A is the set of all regular cardinals between two cardinals), then pcf(A) is also an interval of regular cardinals and |pcf(A)|<|A|+4...

successor cardinal or a limit cardinal, and either a regular cardinal or a singular cardinal. A great many sets studied in mathematics have cardinality equal...

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...

zero Lebesgue (or other) measure Singular cardinal, an infinite cardinal number that is not a regular cardinal Singular point of a curve, in geometry Singularity...

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

nonrecursive ordinal, also called the Church–Kleene ordinal). Any regular uncountable cardinal is an admissible ordinal. By a theorem of Sacks, the countable...

that the only constraints on permissible values for 2κ when κ is a regular cardinal are κ < cf ⁡ ( 2 κ ) {\displaystyle \kappa <\operatorname {cf} (2^{\kappa...

(\kappa )>\kappa } for all infinite cardinals κ {\displaystyle \kappa } by König's theorem. For regular cardinals κ {\displaystyle \kappa } , ℷ ( κ )...

infinite regular cardinal. A regular ordinal is an ordinal that is equal to its cofinality. A singular ordinal is any ordinal that is not regular. Every...

The Arizona Cardinals are a professional American football team based in the Phoenix metropolitan area. The Cardinals compete in the National Football...

Jensen showed that in the constructible universe for any uncountable regular cardinal κ there is a κ-Kurepa tree unless κ is ineffable. A Kurepa tree can...

\omega _{2}} is a regular cardinal. If 0 ♯ {\displaystyle 0^{\sharp }} does not exist, it also follows that the singular cardinals hypothesis holds.p...

forcing to determine the possible values of the continuum function at regular cardinals. Iterated forcing with countable support was investigated by Laver...

clerics regular or clerks regular are clerics (mostly priests) who are members of a religious order under a rule of life (regular). Clerics regular differ...

principle at a singular strong limit cardinal—in fact, at all singular cardinals and all regular successor cardinals—it implies that the axiom of determinacy...

theory, the aleph numbers are a sequence of numbers used to represent the cardinality (or size) of infinite sets. They were introduced by the mathematician...

priest, I said nine Masses, and that is regular in the Philippines." Discussing priestly celibacy, Cardinal Angelo Scola, the synod moderator, expressed...

\kappa \,} is a regular cardinal then club sets are also closed under diagonal intersection. In fact, if κ {\displaystyle \kappa \,} is regular and F {\displaystyle...

prefect of the Supreme Tribunal of the Apostolic Signatura. He was made a cardinal in 2010. A canon lawyer, Burke is perceived as a voice of traditionalism...

and has served as a member of the Council of Cardinals since 2014, the same year he was made a cardinal. Before his tenure as secretary of state, Parolin...

particularly on the cardinal properties and Vopěnka's principle. Let κ {\displaystyle \kappa } be an infinite regular cardinal, i.e. a cardinal number that is...

the privileges of the cardinal bishop. In 1914, Pius X took steps to regulate the irregularities in the incomes of the six cardinal suburbicarian bishops...

These characters appear in the American animated television series Regular Show, created by J. G. Quintel for Cartoon Network. The series revolves around...