Definition of Ultrapowers. Meaning of Ultrapowers. Synonyms of Ultrapowers

- 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...
- a Project Gemini spacecraft incident. The cosmic radiation gave him "ultrapowers" (rather than superpowers), and so Ultiman set out to do good in the...
- which ended up altering him both mentally and physically, giving him "ultrapowers" similar to Superman's superpowers. According to Alexander Luthor, the...
- model that can be constructed from the ordinary natural numbers via the ultrapower construction. Other generalizations are discussed in Number § Extensions...
- 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:...
- spaces, and in model theory in the construction of ultraproducts and ultrapowers. Every ultrafilter on a compact Hausdorff space converges to exactly...
- itself a model of that theory, and thus if two models have isomorphic ultrapowers, they are elementarily equivalent. The Keisler-Shelah theorem provides...
- types as may be "reasonably expected" given its size. For example, an ultrapower model of the hyperreals is ℵ 1 {\displaystyle \aleph _{1}} -saturated...
- 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...