In set theory, a supercompact cardinal is a type of large cardinal independently introduced by Solovay and Reinhardt.[1] They display a variety of reflection properties.
^A. Kanamori, "Kunen and set theory", pp.2450--2451. Topology and its Applications, vol. 158 (2011).
and 24 Related for: Supercompact cardinal information
In set theory, a supercompactcardinal is a type of large cardinal independently introduced by Solovay and Reinhardt. They display a variety of reflection...
In mathematics, the term supercompact may refer to: In set theory, a supercompactcardinal In topology, a supercompact space. This disambiguation page...
In set theory, a strong cardinal is a type of large cardinal. It is a weakening of the notion of a supercompactcardinal. If λ is any ordinal, κ is λ-strong...
implied by supercompactness. Given that the relevant cardinals exist, it is consistent with ZFC either that the first measurable cardinal is strongly...
huge cardinal implies the consistency of a supercompactcardinal, nevertheless, the least huge cardinal is smaller than the least supercompactcardinal (assuming...
existence of a supercompactcardinal, but assuming both exist, the first huge is smaller than the first supercompact. Large cardinals are understood in...
C(n)-extendible cardinals for all n (Bagaria 2011). All extendible cardinals are supercompactcardinals (Kanamori 2003). List of large cardinal properties...
weaker versions of strong and supercompactcardinals, consistent with V = L. Many theorems related to these cardinals have generalizations to their unfoldable...
Although the definition is similar to one of the definitions of supercompactcardinals, the elementary embedding here only has to exist in V [ G ] {\displaystyle...
subcompact cardinals implies existence of many 1-extendible cardinals, and hence many superstrong cardinals. Existence of a 2κ-supercompactcardinal κ implies...
Compact cardinal may refer to: Weakly compact cardinal Subcompact cardinalSupercompactcardinal Strongly compact cardinal This article includes a list...
2^{\kappa }=\kappa ^{+}} . Starting with κ {\displaystyle \kappa } a supercompactcardinal, Silver was able to produce a model of set theory in which κ {\displaystyle...
no=10 no=11 no=12 no=13 no=14 no=15 no=16 supercompact A supercompactcardinal is an uncountable cardinal κ such that for every A such that Card(A) ≥...
with supercompactcardinals. If κ is a supercompactcardinal, a Laver function is a function ƒ:κ → Vκ such that for every set x and every cardinal λ ≥ |TC(x)| + κ...
consistency of the existence of a strongly compact cardinal imply the consistent existence of a supercompactcardinal? Does there exist a Jónsson algebra on ℵω...
and hence existence of inner models with many Woodin cardinals. If there is a supercompactcardinal, then there is a model of set theory in which PFA holds...
54: 67–71. doi:10.4064/fm-54-1-67-71. Woodin, W. Hugh (1988). "Supercompactcardinals, sets of reals, and weakly homogeneous trees". Proceedings of the...
inaccessible cardinals Existence of Mahlo cardinals Existence of measurable cardinals (first conjectured by Ulam) Existence of supercompactcardinals The following...
Hypothesis, the $\Omega$ Conjecture, and the inner model problem of one supercompactcardinal The Eighteenth Annual Gödel Lecture 2007 Ehud Hrushovski (a lecture...
regular cardinal. He proved that the least strongly compact cardinal can be equal to the least measurable cardinal or to the least supercompactcardinal (but...
the consistency of a supercompactcardinal, it is possible to construct a model where 2κ = κ++ holds for some measurable cardinal κ. With the introduction...
Global Information