一般而言，高校数学教员今天就要上班了，在数学教研室开个会议，安排相关工作。在会议上，微积分手机版也许被提及。
实质上（也是实在话），微积分手机版就是一种“超乘积结构”的自然语言变形，这是模型论的断言。
什么是“超乘积结构”？请读者参阅J.Keisler院士近年来发表的论文（本本附件）。
袁萌 陈启清 8月27日
附：THE ULTRAPRODUCT CONSTRUCTION（J.KEISLER发表于2012.06.05）
Abstract. This is a brief survey of the ultraproduct construction, which is meant to provide background material for the readers of this volume.
1. Introduction
The ultraproduct construction is a uniform method of building models of first order theories which has applications in many areas of mathematics. It is attractive because it is algebraic in nature, but preserves all properties expressible in first order logic. The idea goes back to the construction of nonstandard models of arithmetic by Skolem [51] in 1934. In 1948, Hewitt [16] studied ultraproducts of fields. For first order structures in general, the ultraproduct construction was defined by L o´s [37] in 1955. The subject developed rapidly beginning in 1958 with a series of abstracts by Frayne, Morel, Scott, and Tarski（塔尔斯基）, which led to the 1962 paper [14]. Other early papers are [31] by Kochen, and [18] by the author. The groundwork for the application of ultraproducts to mathematics was laid in the late 1950’s through the 1960’s. The purpose of this article is to give a survey of the classical results on ultraproducts of first order structures in order to provide some background for the papers in this volume. （以下省略）