The spectrum of ?31-soundness

被引：1

作者：

Aguilera, J. P. ^{[1
,2
]}

Pakhomov, F. ^{[2
,3
]}

机构：

[1] Vienna Univ Technol, Inst Discrete Math & Geometry, Wiedner Hauptstr 8-10, A-1040 Vienna, Austria

[2] Univ Ghent, Dept Math, Krijgslaan 281-S8, B-9000 Ghent, Belgium

[3] Russian Acad Sci, Steklov Math Inst, Ulitsa Gubkina 8, Moscow 117966, Russia

来源：

PHILOSOPHICAL TRANSACTIONS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES | 2023年 / 381卷 / 2248期

基金：

奥地利科学基金会;

关键词：

sound theory; ptyx; ordinal number;

D O I：

10.1098/rsta.2022.0013

中图分类号：

O [数理科学和化学]; P [天文学、地球科学]; Q [生物科学]; N [自然科学总论];

学科分类号：

07 ; 0710 ; 09 ;

摘要：

We study the ?(1)(3)-soundness spectra of theories. Given a recursively enumerable extension T of ACA(0), O-3(1)(T) is defined as the set of all 2-ptykes on which T is correct about well foundedness. This is a measure of how close T is to being ?(1)(3)-sound. We carry out a proof theoretic classification of theories according to O-3(1)(T), as well as a characterization of the sets of the form O-3(1)(T) n ?(0)(1). Many of the results generalize ton greater than 3.

引用

页数：18