- same signature. The
ultrapower is the
special case of this
construction in
which all
factors are equal. For example,
ultrapowers can be used to construct...
- for all
hyperintegers H {\displaystyle H} . The
transfer principle for
ultrapowers is a
consequence of Łoś's
theorem of 1955.
Concerns about the soundness...
- as a complement. D-media
Communication Tech (a
subsidiary company of
Ultrapower Software Co., Ltd)
undertakes construction,
operation and
maintain of...
-
Incoming champions –
Sinner and
Saint (Judas
Icarus and
Travis Williams) Date
Winner Event/Show Note(s)
January 11
UltraPOWER! (Amira and Jaiden)
Roseland X...
-
hyperinteger is
given by the
class of the
sequence (1, 2, 3, ...) in the
ultrapower construction of the hyperreals. The
standard integer part function: ⌊...
-
nonstandard analysis also use the
concept of
internal sets.
Relative to the
ultrapower construction of the
hyperreal numbers as
equivalence classes of sequences...
- are
order isomorphic. This
unique field Ϝ can be
defined by
means of an
ultrapower, as R N / M {\displaystyle \mathbb {R} ^{\mathbb {N} }/\mathbf {M} } ...
-
equivalence class of the
identity function on κ maps to κ
itself in the
ultrapower construction. Equivalently, if f:κ→κ is such that f(α)<α for most α<κ...
-
types as may be "reasonably expected"
given its size. For example, an
ultrapower model of the
hyperreals is ℵ 1 {\displaystyle \aleph _{1}} -saturated...
- the
ultrapower construction from
model theory.
Since V is a
proper class, a
technical problem that is not
usually present when
considering ultrapowers needs...
