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Type of cardinal number in mathematics
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
Regular_cardinal
Type of infinite number in set theory
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
Inaccessible_cardinal
Topics referred to by the same term
sets Partition regularity Regular cardinal, a cardinal number that is equal to its cofinality Regular modal logic Regular conditional probability, a
Regular
Size of a possibly infinite set
In mathematics, a cardinal number, or cardinal for short, is a kind of number that measures the cardinality of a set, i.e., how many elements there are
Cardinal_number
Generalization of "n-th" to infinite cases
cardinal precisely when the set of regular cardinals below it is stationary. By relaxing the condition on the limit cardinals, one defines a cardinal
Ordinal_number
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
Pcf_theory
Type of large transfinite number
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
Mahlo_cardinal
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
Strongly_compact_cardinal
Mathematical theorem in set theory
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
Easton's_theorem
Catholic religious institute
with the blessing of the Resurrectionists and Cardinal Francis George, Phillips founded the Canons Regular of St. John Cantius. They were formally established
Canons Regular of St. John Cantius
Canons_Regular_of_St._John_Cantius
Mathematical logic concept
absolute: being countable being a cardinal being a regular cardinal being a limit cardinal being an inaccessible cardinal Skolem's paradox is the seeming
Absoluteness_(logic)
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
Remarkable_cardinal
Set-theoretic tree with uncountable branches
Jensen showed that in the constructible universe for any uncountable regular cardinal κ {\displaystyle \kappa } there is a κ {\displaystyle \kappa } -Kurepa
Kurepa_tree
Theorem in axiomatic set theory
(\kappa )>\kappa } for all infinite cardinals κ {\displaystyle \kappa } by König's theorem. For regular cardinals κ {\displaystyle \kappa } , ℷ ( κ )
Gimel_function
NFL team in Phoenix, Arizona
The Arizona Cardinals are a professional American football team based in the Phoenix metropolitan area. The Cardinals compete in the National Football
Arizona_Cardinals
nonrecursive ordinal, also called the Church–Kleene ordinal). Any regular uncountable cardinal is an admissible ordinal. By a theorem of Sacks, the countable
Admissible_ordinal
forcing to determine the possible values of the continuum function at regular cardinals. Iterated forcing with countable support was investigated by Laver
List_of_forcing_notions
Concept in set theory
\omega _{2}} is a regular cardinal. If 0 ♯ {\displaystyle 0^{\sharp }} does not exist, it also follows that the singular cardinals hypothesis holds.p
Zero_sharp
These characters appear in the American animated television series Regular Show, created by J. G. Quintel for Cartoon Network. The series revolves around
List of Regular Show characters
List_of_Regular_Show_characters
Size of subsets in order theory
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
Cofinality
Catholic clergy belonging to a religious order
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
Cleric_regular
Topics referred to by the same term
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
Singular
American actor (born 1959)
Farragut on Helix (2014–15). Campbell starred as Det. John Cardinal on the Canadian CTV series Cardinal, for which he won three Canadian Screen Awards. He is
Billy_Campbell
Cardinality of the set of real numbers
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
Cardinality_of_the_continuum
Roman Catholic priests living in community under a religious rule
dispersed, according to Cardinal Gasquet's computation, ninety-one houses in all. In the early 20th century, the canons regular were represented in England
Canon_regular
Function that returns cardinal numbers
mathematics, a cardinal function (or cardinal invariant) is a function that returns cardinal numbers. The most frequently used cardinal function is the
Cardinal_function
Mathematical concept
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
Ramsey_cardinal
American mathematician (born 1938)
holds; Proving that if κ {\displaystyle \kappa } is an uncountable regular cardinal, and S ⊆ κ {\displaystyle S\subseteq \kappa } is a stationary set,
Robert_M._Solovay
Canadian actress
Tantoo Cardinal (born July 20, 1950) is a Canadian actress of Cree and Métis heritage. In 2009 she was made a member of the Order of Canada "for her contributions
Tantoo_Cardinal
regular strong limit cardinal 2. A strongly Mahlo cardinal is a strongly inaccessible cardinal such that the set of strongly inaccessible cardinals below
Glossary_of_set_theory
Infinite cardinal number
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
Aleph_number
Ordinals in mathematics and set theory
inaccessible or recursively Mahlo ordinals is a theorem of ZFC: in fact, any regular cardinal is recursively Mahlo and more, but even if we limit ourselves to countable
Large_countable_ordinal
Problem in set theory
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
Suslin's_problem
Hierarchy of formulas in set theory
{\displaystyle (x,\in )} p. 29 x is a cardinal x is a regular cardinal x is a limit cardinal x is an inaccessible cardinal. x is the powerset of y x is V α
Lévy_hierarchy
American college soccer season
2025 Stanford Cardinal women's soccer team represented Stanford University during the 2025 NCAA Division I women's soccer season. The Cardinal were led by
2025 Stanford Cardinal women's soccer team
2025_Stanford_Cardinal_women's_soccer_team
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
Accessible_category
American basketball player (born 2001)
Basketball Association (NBA). He played college basketball for the Stanford Cardinal. Jones attended Bishop Miege in Roeland Park, Kansas, emerging as a key
Spencer_Jones_(basketball)
implies stationary reflection, i.e., if S is a stationary subset of some regular cardinal κ ≥ ω2 and every element of S has countable cofinality, then there
Martin's_maximum
Size of a set in mathematics
In mathematics, cardinality is an inherent property of sets, roughly meaning the number of individual objects they contain, which may be infinite. The
Cardinality
Set theory concept
\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
Club_set
\operatorname {Hom} (X,-)} commutes with κ-filtered colimits. 2. Given a regular cardinal κ, a category is κ-accessible if it has κ-filtered colimits and there
Glossary_of_category_theory
American college basketball team
Pac-10 regular-season title, and reached the Sweet Sixteen. Stanford's rise to national prominence culminated in the 1989–90 season, when the Cardinal captured
Stanford Cardinal women's basketball
Stanford_Cardinal_women's_basketball
Mathematical measure for topological spaces
measurable cardinal with the discrete topology has a Borel probability measure such that every compact subset has measure 0, so this measure is outer regular but
Regular_measure
Set-theoretic function
ordinal functions ψκ indexed by uncountable regular cardinals κ smaller than the least weakly Mahlo cardinal M0 introduced by German mathematician Gerhard
Ordinal_collapsing_function
American Catholic cardinal (born 1948)
prefect of the Supreme Tribunal of the Apostolic Signatura. He was made a cardinal in 2010. A canon lawyer, Burke is a major voice of traditionalism among
Raymond_Leo_Burke
American college football organization
Mayfield in 2017. As of September 10, 2025, 271 former Cardinal have played in an NFL or AFL regular-season game. Stanford first fielded a football team
Stanford_Cardinal_football
Method for constructing models of set theory
construct models where Martin's axiom holds and the continuum is any given regular cardinal. In iterated forcing, one has a transfinite sequence Pα of forcing
Iterated_forcing
Major League Baseball season
The Cardinals released their 2026 schedule on August 26, 2025. For one of the few times in the past dozen years, the Cardinals opened the regular season
2026 St. Louis Cardinals season
2026_St._Louis_Cardinals_season
Tree in set theory
Kurepa (1935). A cardinal κ for which no κ-Aronszajn trees exist is said to have the tree property (sometimes the condition that κ is regular and uncountable
Aronszajn_tree
Stadium at the University of Louisville
Stadium, also known as L&N Stadium and formerly known as Cardinal Stadium and Papa John's Cardinal Stadium, is a football stadium located in Louisville,
L&N Federal Credit Union Stadium
L&N_Federal_Credit_Union_Stadium
Theorem in set theory
{cf} (\kappa )}} . If κ is regular, then this follows from Cantor's theorem. If κ is singular, then κ is a limit cardinal. Choose a strictly increasing
Kőnig's_theorem_(set_theory)
American baseball player (born 1994)
League Baseball (MLB). He has previously played in MLB for the St. Louis Cardinals, New York Yankees, Cincinnati Reds, New York Mets, Minnesota Twins, and
Harrison_Bader
Class of cardinal numbers
mathematics, limit cardinals are certain cardinal numbers. A cardinal number λ is a weak limit cardinal if λ is neither a successor cardinal nor zero. This
Limit_cardinal
diagram d : D → J {\displaystyle d:D\to J} . Extending this, given a regular cardinal κ, a category J {\displaystyle J} is defined to be κ-filtered if there
Filtered_category
Number that is larger than all finite numbers
larger than all finite numbers. These include the transfinite cardinals, which are cardinal numbers used to quantify the size of infinite sets, and the
Transfinite_number
nontrivial relations can be proved between them, most cardinal invariants can be any regular cardinal between ℵ1 and 2ℵ0. This is a major area of study in
List of statements independent of ZFC
List_of_statements_independent_of_ZFC
first-order objects having cardinality ω1, and the predicate for cardinality ω2, and so on for infinite regular cardinals. Graphs of bounded tree width
S2S_(mathematics)
Intercollegiate basketball season
Stanford Cardinal women's basketball team represented Stanford University in the 2011–12 NCAA Division I women's basketball season. The Cardinal, coached
2011–12 Stanford Cardinal women's basketball team
2011–12_Stanford_Cardinal_women's_basketball_team
Major League Baseball season
The Cardinals released their 2025 schedule on July 18, 2024. For one of the few times in the past dozen years, the Cardinals opened the regular season
2025 St. Louis Cardinals season
2025_St._Louis_Cardinals_season
Major League Baseball rivalry
Dodgers Cardinals The Cardinals–Dodgers rivalry is a Major League Baseball (MLB) National League rivalry played between the St. Louis Cardinals and the
Cardinals–Dodgers_rivalry
least β-Silver cardinal strictly greater than α has cofinality ω in V. All Silver cardinals are regular ordinals in L. Silver cardinal is stronger than
Silver_cardinal
Species of bird
closely resembles the northern cardinal and the vermilion cardinal, which are in the same genus. The desert cardinal is one of three birds in the genus
Pyrrhuloxia
Kind of large cardinal number
definitions, κ {\displaystyle \kappa } will always be a regular uncountable cardinal number. A cardinal number κ {\displaystyle \kappa } is called almost ineffable
Ineffable_cardinal
{\displaystyle \omega } . For uncountable regular cardinals κ {\displaystyle \kappa } (and some other cardinals) this can be strengthened to κ → ( κ , ω
Erdős–Dushnik–Miller_theorem
American college basketball season
finished 17–1, only losing to Washington in the last game of the regular season. The Cardinal won the Pac-10 tournament defeating Washington State, next Oregon
2004–05 Stanford Cardinal men's basketball team
2004–05_Stanford_Cardinal_men's_basketball_team
American football player (born 1983)
regular season, Arizona Cardinals". StatMuse. Retrieved March 27, 2025. "Career games with at least 100 receiving yards, playoffs, Arizona Cardinals"
Larry_Fitzgerald
American baseball player and coach (born 1980)
February 9, 2009, Cardinal second baseman Adam Kennedy was released by the club, which sparked discussion about placing Schumaker as the regular second baseman
Skip_Schumaker
Varsity volleyball team
history. In Cruz's first year as head coach, he led the Cardinals to their first MIVA regular season championship, conference tournament championship
Ball State Cardinals men's volleyball
Ball_State_Cardinals_men's_volleyball
are defined for maps of spectra. Let α {\displaystyle \alpha } be a regular cardinal. A morphism f : x → y {\displaystyle f:x\to y} in the homotopy category
Phantom_map
American football coach (born 1983)
against the Denver Broncos on August 11, 2023. However, the Cardinals lost in Gannon's regular-season debut against the Washington Commanders by a score
Jonathan_Gannon
Israeli mathematician
regular cardinal. He proved that the least strongly compact cardinal can be equal to the least measurable cardinal or the least supercompact cardinal
Menachem_Magidor
Subfield of set theory
with ordinal definable payoff and length ω implies that for every regular cardinal κ>ω there are no ordinal definable disjoint stationary subsets of κ
Determinacy
Yugoslavian mathematician
model of MA + ¬wKH in a way to allow him to make the continuum any regular cardinal, and so derived a variety of topological consequences. Here MA is an
Stevo_Todorčević
American baseball manager (born 1986)
Central. The Cardinals lost to the Phillies 2–0 in the NL Wild Card Series. Before the 2024 regular season began, Marmol and the Cardinals agreed to a
Oliver_Marmol
American football player (born 1992)
1992) is an American professional football quarterback for the Arizona Cardinals of the National Football League (NFL). Following a stint with the Florida
Jacoby_Brissett
Texas college athletics team
The Lamar Cardinals and Lady Cardinals (variously Cardinals or Cards) refers to the college athletics teams of Lamar University, in Beaumont, Texas. The
Lamar Cardinals and Lady Cardinals
Lamar_Cardinals_and_Lady_Cardinals
American college soccer season
defeated during the regular season. The Tigers avenged that regular season loss and advanced to the Semifinals, while the Cardinal were eliminated from
2024 Stanford Cardinal men's soccer team
2024_Stanford_Cardinal_men's_soccer_team
partially ordered set P {\displaystyle P} is proper if for all regular uncountable cardinals λ {\displaystyle \lambda } , forcing with P preserves stationary
Proper_forcing_axiom
Intercollegiate basketball season
Stanford Cardinal women's basketball team represented Stanford University in the 2010–11 NCAA Division I women's basketball season. The Cardinal, coached
2010–11 Stanford Cardinal women's basketball team
2010–11_Stanford_Cardinal_women's_basketball_team
Mahlo cardinals M {\displaystyle M} to generate large countable ordinals. A weakly Mahlo cardinal is a cardinal such that the set of regular cardinals below
Rathjen's_psi_function
American college basketball season
eighteenth and final season with the Cardinal. The Cardinal were a member of the Pacific-10 Conference and were the Pac-10 regular season champions as well as
2003–04 Stanford Cardinal men's basketball team
2003–04_Stanford_Cardinal_men's_basketball_team
College soccer team
The Ball State Cardinals women's soccer team represents Ball State University in women's soccer. The school competes in the Mid-American Conference in
Ball State Cardinals women's soccer
Ball_State_Cardinals_women's_soccer
Major League Baseball franchise
The St. Louis Cardinals are an American professional baseball team based in St. Louis. The Cardinals compete in Major League Baseball (MLB) as a member
St._Louis_Cardinals
Type of totally ordered set
isomorphism) is the ordered set of rational numbers. Suppose that κ = ℵα is a regular cardinal and let X be the set of all functions f from κ to {−1,0,1} such that
Η_set
Catholic organization in West Virginia, US
of Wheeling-Charleston. The institute was founded by then-Bishop (later Cardinal) Raymond Leo Burke and Dom Daniel Augustine Oppenheimer, Prior. This institute
Canons Regular of the New Jerusalem
Canons_Regular_of_the_New_Jerusalem
American college football season
coach Scott Satterfield. The Cardinals played their home games at Cardinal Stadium, formerly known as Papa John's Cardinal Stadium, in Louisville, Kentucky
2020 Louisville Cardinals football team
2020_Louisville_Cardinals_football_team
American college basketball season
the regular season on a high, winning their final four games. The final two games were road victories over Notre Dame and NC State. The Cardinal finished
2025–26 Stanford Cardinal men's basketball team
2025–26_Stanford_Cardinal_men's_basketball_team
measurable cardinals below κ which is regular, and thus κ is a limit of κ-many measurable cardinals. Strong cardinals also lie below superstrong cardinals and
Strong_cardinal
Catholic religious order
Benedict. From this comes the title "regular", meaning one following a "rule" (Latin: regula). Under the guidance of Cardinal Hildebrand of Sovana (later to
Canons_Regular_of_the_Lateran
American Catholic prelate (1930–2025)
in a canonical trial. Prior to his dismissal, he served as a bishop and cardinal, holding the positions of Archbishop of Newark from 1986 to 2000 and Archbishop
Theodore_McCarrick
Catholic appointments from 1703 to 1720
on 11 February 1704), then cardinal-bishop of Sabina (26 April 1719), cardinal-bishop of Frascati (12 June 1724), cardinal-bishop of Porto e S. Rufina
Cardinals created by Clement XI
Cardinals_created_by_Clement_XI
Stanford considers the 1950 Pineapple Bowl a game of the 1949 regular season "Stanford Cardinal Football Record by Year". "What is the history of Stanford's
List of Stanford Cardinal football seasons
List_of_Stanford_Cardinal_football_seasons
Hungarian set theorist
models L(A) (see relative constructibility), and proved that if κ is a regular cardinal and A is a subset of κ+, then ZFC and 2κ = κ+ hold in L(A). This can
András_Hajnal
Italian Catholic Augustinian canon regular
6 February 1158) was an Italian Catholic Augustinian canon regular and also the Cardinal-Bishop of Palestrina from December 1144 after his relative Pope
Guarinus_of_Palestrina
Intercollegiate basketball season
Stanford Cardinal women's basketball team represented Stanford University during the 2013–14 NCAA Division I women's basketball season. The Cardinal, led
2013–14 Stanford Cardinal women's basketball team
2013–14_Stanford_Cardinal_women's_basketball_team
American college basketball season
Stanford Cardinal men's basketball team represented Stanford University during the 2007–08 NCAA Division I men's basketball season. The Cardinal were led
2007–08 Stanford Cardinal men's basketball team
2007–08_Stanford_Cardinal_men's_basketball_team
Major League Baseball rivalry
1969, and later three divisions in 1994, the Cardinals and Cubs remained together. The Cubs lead the regular season series 1,286–1,231–19. The teams' lone
Cardinals–Cubs_rivalry
Intercollegiate basketball season
sixteen. The Stanford Cardinal finished the 2013-14 season with an overall record of 33–4, with a record of 17–1 in the Pac-12 regular season to win their
2014–15 Stanford Cardinal women's basketball team
2014–15_Stanford_Cardinal_women's_basketball_team
French footballer (born 1997)
Lens had signed Le Cardinal in a "joker" transfer, a type of transfer allowed by the Ligue de Football Professionnel outside the regular transfer window
Julien_Le_Cardinal
Athletic facility at North Central College
previous year. The Fire finished the 2002 regular season with an average of 12,922 spectators at Cardinal Stadium, including four consecutive sellouts
Benedetti–Wehrli_Stadium
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