- In set theory, a
supercompact cardinal 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
supercompact cardinal In topology, a
supercompact space. This
disambiguation page...
- concept.
Strong compactness implies measurability, and is
implied by
supercompactness.
Given that the
relevant cardinals exist, it is
consistent with ZFC...
- mathematics, in the
field of topology, a
topological space is
called supercompact if
there is a
subbasis such that
every open
cover of the topological...
-
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
means that κ is a cardinal...
- down.) subcompact,
strongly compact (Woodin<
strongly compact≤
supercompact),
supercompact,
hypercompact cardinals η-extendible,
extendible cardinals almost...
-
implies the
consistency of a
supercompact cardinal, nevertheless, the
least huge
cardinal is
smaller than the
least supercompact cardinal (****uming both exist)...
- than the
existence of a
supercompact cardinal, but ****uming both exist, the
first huge is
smaller than the
first supercompact.
Large cardinals are understood...
- } .
Although the
definition is
similar to one of the
definitions of
supercompact cardinals, the
elementary embedding here only has to
exist in V [ G ]...
- are
supercompact cardinals (Kanamori 2003). List of
large cardinal properties Reinhardt cardinal Magidor, M. (1971). "On the Role of
Supercompact and...
