-
hyperreal fields we
obtain in this case are
called ultrapowers of R and are
identical to the
ultrapowers constructed via free
ultrafilters in
model theory...
- 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...
-
which ended up
altering him both
mentally and physically,
giving him "
ultrapowers"
similar to Superman's superpowers.
According to
Alexander Luthor, the...
- a
Project Gemini spacecraft incident. The
cosmic radiation gave him "
ultrapowers" (rather than superpowers), and so
Ultiman set out to do good in the...
- mouse; its
iterated ultrapowers are
vacuously well-founded
because there are no
extenders on its
sequence with
which to take an
ultrapower. T. Jech, Set Theory:...
-
model that can be
constructed from the
ordinary natural numbers via the
ultrapower construction.
Other generalizations are
discussed in
Number § Extensions...
- 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...
- spaces, and in
model theory in the
construction of
ultraproducts and
ultrapowers.
Every ultrafilter on a
compact Hausdorff space converges to exactly...
- the
ultrapower construction from
model theory.
Since V is a
proper class, a
technical problem that is not
usually present when
considering ultrapowers needs...
-
itself a
model of that theory, and thus if two
models have
isomorphic ultrapowers, they are
elementarily equivalent. The Keisler-Shelah
theorem provides...
