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...

inaccessible cardinal". An uncountable cardinal is weakly inaccessible if it is a regular weak limit cardinal. It is strongly inaccessible, or just inaccessible...

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

a limit ordinal. Using von Neumann cardinal assignment, every infinite cardinal number is also a limit ordinal. Various other ways to define limit ordinals...

a successor cardinal. Cardinals that are not successor cardinals are called limit cardinals; and by the above definition, if λ is a limit ordinal, then...

successor cardinal or a limit cardinal. Some cardinalities cannot be proven to be equal to any particular aleph, for instance the cardinality of the continuum...

1586, divided among fourteen cardinal-deacons, fifty cardinal-priests, and six cardinal-bishops. Popes respected that limit until Pope John XXIII increased...

A cardinal (Latin: Sanctae Romanae Ecclesiae cardinalis; lit. 'cardinal of the Holy Roman Church') is a senior member of the clergy of the Catholic Church...

limit 1.  A (weak) limit cardinal is a cardinal, usually assumed to be nonzero, that is not the successor κ+ of another cardinal κ 2.  A strong limit...

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...

infinite cardinal κ having cofinality ℵ0 means that there is a (countable-length) sequence κ0 ≤ κ1 ≤ κ2 ≤ ... of cardinals κi < κ whose limit (i.e. its...

is a strong limit cardinal, which completes the proof of its inaccessibility. Although it follows from ZFC that every measurable cardinal is inaccessible...

\omega _{n}} for natural numbers n (any limit of cardinals is a cardinal, so this limit is indeed the first cardinal after all the ω n {\displaystyle \omega...

be a singular cardinal. According to Mitchell (1992), the singular cardinals hypothesis is: If κ is any singular strong limit cardinal, then 2κ = κ+....

 2005–2013) created 90 cardinals in five consistories. With three of those consistories he respected the limit on the number of cardinal electors set at 120...

In mathematics, the inverse limit (also called the projective limit) is a construction that allows one to "glue together" several related objects, the...

uncountable strong limit cardinal is not satisfied in such a model; thus the existence of ℶω (the smallest uncountable strong limit cardinal) cannot be proved...

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...

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...

The cardinal virtues are four virtues of mind and character in both classical philosophy and Christian theology. They are prudence, justice, fortitude...

{\displaystyle \lambda } is a limit ordinal. The cardinal ℶ 0 = ℵ 0 {\displaystyle \beth _{0}=\aleph _{0}} is the cardinality of any countably infinite set...

singular cardinal λ {\displaystyle \lambda } ? Does the generalized continuum hypothesis imply the existence of an ℵ2-Suslin tree? If ℵω is a strong limit cardinal...

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...

larger than all finite numbers. These include the transfinite cardinals, which are cardinal numbers used to quantify the size of infinite sets, and the...

theory. The least worldly κ that is a limit of worldly cardinals (equivalently, a limit of κ worldly cardinals). The least worldly κ and λ with Vκ ≺Σ2...

 March 1473 – 29 November 1530) was an English statesman and Catholic cardinal. When Henry VIII became King of England in 1509, Wolsey became the king's...

natural numbers n {\displaystyle n} (any limit of cardinals is a cardinal, so this limit is indeed the first cardinal after all the ω n {\displaystyle \omega...

In mathematics, cardinality describes a relationship between sets which compares their relative size. For example, the sets A = { 1 , 2 , 3 } {\displaystyle...

Reflecting cardinals were introduced by (Mekler & Shelah 1989). Every weakly compact cardinal is a reflecting cardinal, and is also a limit of reflecting...

the cardinality of x. Then for any universe U, c(U) is either zero or strongly inaccessible. Assuming it is non-zero, it is a strong limit cardinal because...