-
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...
- 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:...
-
indispensable (even in the
presence of the
axiom of choice) when
taking ultrapowers of
proper classes in
model theory. (Kanamori 1994:47) The use of Scott's...
-
model that can be
constructed from the
ordinary natural numbers via the
ultrapower construction.
Other generalizations are
discussed in
Number § Extensions...
-
ended up
altering the
human 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...
- 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
equivalence class [(0.9, 0.99, 0.999, ...)] of this
sequence in the
ultrapower construction,
which is a
number that
falls short of 1 by an infinitesimal...
