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

[1] Parameter-free uniformisation
Friedman, Sy-David
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2008, 136 (09) : 3327 - 3330
[2] PARAMETER-FREE STYLE PROJECTION FOR ARBITRARY IMAGE STYLE TRANSFER
Huang, Siyu
Xiong, Haoyi
Wang, Tianyang
Wen, Bihan
Wang, Qingzhong
Chen, Zeyu
Huan, Jun
Dou, Dejing
2022 IEEE INTERNATIONAL CONFERENCE ON ACOUSTICS, SPEECH AND SIGNAL PROCESSING (ICASSP), 2022, : 2070 - 2074
[3] Approaching a parameter-free metadynamics
Dickson, Bradley M.
PHYSICAL REVIEW E, 2011, 84 (03):
[4] PARAMETER-FREE UNIVERSAL INDUCTION
KAYE, R
ZEITSCHRIFT FUR MATHEMATISCHE LOGIK UND GRUNDLAGEN DER MATHEMATIK, 1989, 35 (05): : 443 - 456
[5] PARAMETER-FREE CLUSTERING MODEL
GITMAN, I
PATTERN RECOGNITION, 1972, 4 (03) : 307 - &
[6] Parameter-free exchange functional
Tsuneda, T
Hirao, K
PHYSICAL REVIEW B, 2000, 62 (23) : 15527 - 15531
[7] Parameter-free polymorphic types
Aehlig, Klaus
ANNALS OF PURE AND APPLIED LOGIC, 2008, 156 (01) : 3 - 12
[8] Parameter-free rendering of single-molecule localization microscopy data for parameter-free resolution estimation
Descloux, Adrien C.
Grussmayer, Kristin S.
Radenovic, Aleksandra
COMMUNICATIONS BIOLOGY, 2021, 4 (01)
[9] Parameter-free rendering of single-molecule localization microscopy data for parameter-free resolution estimation
Adrien C. Descloux
Kristin S. Grußmayer
Aleksandra Radenovic
Communications Biology, 4
[10] Parameter-free Hierarchical Image Segmentation
Abdullah, S. M.
Tischer, Peter
Wijewickrema, Sudanthi
Paplinski, Andrew
2017 IEEE VISUAL COMMUNICATIONS AND IMAGE PROCESSING (VCIP), 2017,

← 1 2 3 4 5 →