Reverse Mathematics and parameter-free Transfer

被引：4

作者：

van den Berg, Benno ^{[1
]}

Sanders, Sam ^{[2
,3
]}

机构：

[1] Univ Amsterdam, Inst for Log Language & Computat, Amsterdam, Netherlands

[2] Tech Univ Darmstadt, Dept Math, Darmstadt, Germany

[3] Univ Leeds, Sch Math, Leeds, W Yorkshire, England

来源：

ANNALS OF PURE AND APPLIED LOGIC | 2019年 / 170卷 / 03期

关键词：

Reverse mathematics; Higher types; Nonstandard analysis;

D O I：

10.1016/j.apal.2018.10.003

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Recently, conservative extensions of Peano and Heyting arithmetic in the spirit of Nelson's axiomatic approach to Nonstandard Analysis, have been proposed. In this paper, we study the Transfer axiom of Nonstandard Analysis restricted to formulas without parameters. Based on this axiom, we formulate a base theory for the Reverse Mathematics of Nonstandard Analysis and prove some natural reversals, and show that most of these equivalences do not hold in the absence of parameter-free Transfer. (C) 2018 Elsevier B.V. All rights reserved.

引用

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页码：273 / 296

页数：24

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