The Use of Ultraproducts in Commutative Algebra, 第 1999 号 12ページ books.google.co.jp/books?id=ohbdke-cBxwC&hl=ja&pg=PA12#v=onepage&q&f=false We will give meaning to the expression a satisfies the formula φ(ξ) in A (sometimes abbreviated to φ(a) holds in A, or is true in A) by induction on the number of quantifiers.