Reverse mathematics and ordinal exponentiation
type: Item
instance of: scholarly article
title: Reverse mathematics and ordinal exponentiation
zbMATH Open document ID: 0791.03034
DOI: 10.1016/0168-0072(94)90076-0
author: Jeffry L. Hirst
published in: Annals of Pure and Applied Logic
publication date: 1994-03-10T00:00:00Z
review text: The paper is devoted to the study of Simpson's claim that ``\(\text{ATR}_ 0\) is the weakest set of axioms which permits the development of a decent theory of countable ordinals''. An empirical support for this thesis is given. It is shown in particular that Cantor's Normal Form Theorem and Sherman's Inequality for countable well-orderings are both equivalent to \(\text{ATR}_ 0\). To obtain the proofs, ordinal exponentiation was developed and the comparability result of Friedman and Hirst was strengthened.
Mathematics Subject Classification ID: 03F35
zbMATH DE Number: 513338
zbMATH Keywords: Cantor's Normal Form Theorem
zbMATH Keywords: Sherman's Inequality for countable well- orderings
zbMATH Keywords: \(\text{ATR}_ 0\)
zbMATH Keywords: ordinal exponentiation
reviewed by: Roman Murawski
MaRDI profile type: Publication
full work available at URL: 0168-0072(94)90076-0
OpenAlex ID: W1987660018
cites work: Q4111536
cites work: Weak comparability of well orderings and reverse mathematics
cites work: Q3773876
cites work: Q3253173
cites work: Which set existence axioms are needed to prove the Cauchy/Peano theorem for ordinary differential equations?
cites work: Q3395521
description: scientific article; zbMATH DE number 513338