MONOTONE SUBSEQUENCE VIA ULTRAPOWER

PIOTR B LASZCZYK, VLADIMIR KANOVEI, MIKHAIL G. KATZ, AND TAHL NOWIK

【摘要】正如陶哲轩(Terence Tao)所指出的那样，一个超积可以成为一个有用的组织原则，为多个层面的问题提供解决方法。在多个层面上展示问题的解决方案。我们把它应用到一个微积分问题的解中:每个无限序列都有一个单调的无限子序列，并且给其他应用。

关键词:序结构;单调子序列;超幂;饱和;紧性

Abstract. An ultraproduct can be a helpful organizing principle in presenting solutions of problems at many levels, as argued by Terence Tao. We apply it here to the solution of a calculus problem: every infinite sequence has a monotone infinite subsequence, and give other applications.

Keywords: ordered structures; monotone subsequence; ultrapower; saturation; compactness

https://doi.org/10.1515/math-2018-0015​doi.orgMatches for: MR=3772690​mathscinet.ams.orghttps://arxiv.org/abs/1803.00312​arxiv.org