微积手机版与超乘积结构
(2018-08-27 05:40:54)微积手机版与超乘积结构
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
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 rst 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 rst 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 elds. For rst order structures in general, the ultraproduct construction was dened 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 rst order structures in order to provide some background for the papers in this volume. (以下省略)