Definition of Ultrapower. Meaning of Ultrapower. Synonyms of Ultrapower

- 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...
- 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: ⌊...
- Icarus and Travis Williams) Date Winner Event/Show Note(s) January 11 UltraPOWER! (Amira and Jaiden) Roseland X April 12 Midnight Heat (Ricky Gibson and...
- 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...
- discovered by Thoralf Skolem (1934). Skolem's method foreshadows the ultrapower construction [...] Several technical issues must be addressed to develop...
- 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...