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

下载

页码：273 / 296

页数：24

共 50 条

[31] Parameter-free expression for superconducting Tc in cuprates
Alexandrov, AS
Kabanov, VV
PHYSICAL REVIEW B, 1999, 59 (21): : 13628 - 13631
[32] A parameter-free adaptive EWMA mean chart
Haq, Abdul
Khoo, Michael B. C.
QUALITY TECHNOLOGY AND QUANTITATIVE MANAGEMENT, 2020, 17 (05): : 528 - 543
[33] A new proposal for a parameter-free integration software
Bernd Spangenberg
Fresenius' Journal of Analytical Chemistry, 1998, 360 : 148 - 151
[34] Parameter-free geometric document layout analysis
Lee, SW
Ryu, DS
IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE, 2001, 23 (11) : 1240 - 1256
[35] Coin Betting and Parameter-Free Online Learning
Orabona, Francesco
Pal, David
ADVANCES IN NEURAL INFORMATION PROCESSING SYSTEMS 29 (NIPS 2016), 2016, 29
[36] Parameter-free coordination numbers for solutions and interfaces
Staub, Ruben
Steinmann, Stephan N.
JOURNAL OF CHEMICAL PHYSICS, 2020, 152 (02):
[37] Parameter-free dissipation in simulated sliding friction
Benassi, A.
Vanossi, A.
Santoro, G. E.
Tosatti, E.
PHYSICAL REVIEW B, 2010, 82 (08)
[38] PARAMETER-FREE FISTA BY ADAPTIVE RESTART AND BACKTRACKING
Bordeaux INP, CNRS, IMB, Talence, France
不详
不详
不详
SIAM J. Optim., 4 (3259-3285): : 3259 - 3285
[39] An Efficient Parameter-Free Learning Automaton Scheme
Di, Chong
Liang, Qilian
Li, Fangqi
Li, Shenghong
Luo, Fucai
IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS, 2021, 32 (11) : 4849 - 4863
[40] A parameter-free similarity graph for spectral clustering
Inkaya, Tulin
EXPERT SYSTEMS WITH APPLICATIONS, 2015, 42 (24) : 9489 - 9498

← 1 2 3 4 5 →