- 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...
-
nonstandard analysis also use the
concept of
internal sets.
Relative to the
ultrapower construction of the
hyperreal numbers as
equivalence classes of sequences...
- do not
contain the
extreme elements of the
parent set. In
terms of the
ultrapower construction, the
hyperreal line *R is
defined as the
collection of equivalence...
-
types as may be "reasonably expected"
given its size. For example, an
ultrapower model of the
hyperreals is ℵ 1 {\displaystyle \aleph _{1}} -saturated...
-
model that can be
constructed from the
ordinary natural numbers via the
ultrapower construction.
Other generalizations are
discussed in
Number § Extensions...
-
hyperinteger is
given by the
class of the
sequence (1, 2, 3, ...) in the
ultrapower construction of the hyperreals. The
standard integer part function: ⌊...
- 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} } ...
-
which ended up
altering him both
mentally and physically,
giving him "
ultrapowers"
similar to Superman's superpowers.
According to
Alexander Luthor, the...
-
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...
