This book, neither assuming nor using any logical formalism, is intended for algebraists and geometers, in the hope of popularizing ultraproducts and their applications in algebra.

... 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 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 ...