... ultraproduct of As modulo U is the quotient of Cart - prod J As by ~ 4 . Definition 11. [ 1 , Definition 2.69 ( Ultraproduct of Sets ) ] ultraproduct U J AS def Cart - prod J A $ / ~ 48 J We write fu to denote the equivalence class that ...

... ultraproduct of the fields Ka modulo U. ( It is useful to notice that the underlying set of the algebraic ultraproduct is independent of the algebraic structure , because only = is used in the definition of the equivalence relation ~ u ...

... ultraproduct of the Cw/O w is isomorphic to C♮/O♮. If almost every Ow is generated by e elements, then so isO♮. In other words, the ultraproduct of ideals Ow ⊆ Cw is equal to the image of the ideal ∏Ow in the product C∞ := ∏Cw ...

... ultraproduct is the classical , or complete ultraproduct . A useful example of a normal ultrapower is the ultrapower reduced to constant functions . Another example : the ultrapower w + Z previously defined from w . 11.8.2 Isomorphism ...

... ultraproduct ) . Let ( M , O ) and w be as above . Define M® ( M , 9 ) to be the normalizer of I ( M , O ) : the set of all xe ( M ) satisfying x1 ( M , O ) c I ( M , O ) and T ( M , 9 ) x ≤ Tw ( M , ø ) . Thus , by definition T1 ( M ...

... ultraproduct construction is that it behaves well when new symbols are added to the vocabulary . The following ... ( Ultraproduct Compactness ) Let S be an infinite set of sentences of L and let I be the set of all finite subsets of ...

... ultraproduct IIY of the Y's as Banach spaces is the 1 - product of the Y's modulo the closed subspace of all elements { } that converge in norm to 0 along a . This ultraproduct is the ultraproduct of Banach spaces discussed in [ He ] ...

... ultraproduct [ 10 ] . This construction is indeed the ultraproduct in the category of Banach spaces and nonexpansive lin- ear maps , and may be telegraphically described using the recipe : take the usual ultraproduct , throw away the ...

... Ultraproct Suppositories Ultraproct Ointment Bioglan Laboratories Limited Spirella Building Bridge Road Letchworth , Herts. been established . However , topical steroids should not be used extensively during the first trimester of preg ...