کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4662458 1633541 2007 23 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
A comparison of well-known ordinal notation systems for ε0
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات منطق ریاضی
پیش نمایش صفحه اول مقاله
A comparison of well-known ordinal notation systems for ε0
چکیده انگلیسی

We consider five ordinal notation systems of ε0 which are all well-known and of interest in proof-theoretic analysis of Peano arithmetic: Cantor’s system, systems based on binary trees and on countable tree-ordinals, and the systems due to Schütte and Simpson, and to Beklemishev.The main point of this paper is to demonstrate that the systems except the system based on binary trees are equivalent as structured systems, in spite of the fact that they have their origins in different views and trials in proof theory. This is true while Weiermann’s results based on Friedman-style miniaturization indicate that the system based on binary trees is of different character than the others.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Annals of Pure and Applied Logic - Volume 147, Issues 1–2, June 2007, Pages 48-70