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

[21] Hierarchical, Parameter-Free Community Discovery
Papadimitriou, Spiros
Sun, Jimeng
Faloutsos, Christos
Yu, Philip S.
MACHINE LEARNING AND KNOWLEDGE DISCOVERY IN DATABASES, PART II, PROCEEDINGS, 2008, 5212 : 170 - +
[22] A parameter-free affinity based clustering
Mukhoty, Bhaskar
Gupta, Ruchir
Lakshmanan, K.
Kumar, Mayank
APPLIED INTELLIGENCE, 2020, 50 (12) : 4543 - 4556
[23] A parameter-free KNN for rating prediction
Fopa, Medjeu
Gueye, Modou
Ndiaye, Samba
Naacke, Hubert
DATA & KNOWLEDGE ENGINEERING, 2022, 142
[24] Parameter-Free Structural Diversity Search
Huang, Jinbin
Huang, Xin
Zhu, Yuanyuan
Xu, Jianliang
WEB INFORMATION SYSTEMS ENGINEERING - WISE 2019, 2019, 11881 : 677 - 693
[25] A Parameter-Free Linear Sampling Method
Liu, Lei
Hu, Guanzhong
IEEE ACCESS, 2019, 7 : 17935 - 17940
[26] Parameter-Free Attention in fMRI Decoding
Qi, Yong
Lin, Huawei
Li, Yanping
Chen, Jiashu
IEEE ACCESS, 2021, 9 (09): : 48704 - 48712
[27] A parameter-free associative classification method
Cerf, Loic
Gay, Dominique
Selmaoui, Nazha
Boulicaut, Jean-Francois
DATA WAREHOUSING AND KNOWLEDGE DISCOVERY, PROCEEDINGS, 2008, 5182 : 293 - +
[28] A parameter-free affinity based clustering
Bhaskar Mukhoty
Ruchir Gupta
Lakshmanan K.
Mayank Kumar
Applied Intelligence, 2020, 50 : 4543 - 4556
[29] Image Analysis in a Parameter-Free Setting
Zhu, Yu
Zeugmann, Thomas
INFORMATION SCIENCES AND SYSTEMS 2015, 2016, 363 : 285 - 294
[30] A CURRENT-FREE AND PARAMETER-FREE CONTROL ALGORITHM
LOSIC, NA
VARGA, LD
IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, 1994, 30 (02) : 324 - 332

← 1 2 3 4 5 →