On Fraïssé's conjecture for linear orders of finite Hausdorff rank
type: Item
instance of: scholarly article
title: On Fraïssé's conjecture for linear orders of finite Hausdorff rank
zbMATH Open document ID: 1184.03006
author: Alberto Marcone
author: Antonio Montalbán
published in: Annals of Pure and Applied Logic
publication date: 2009-10-26T00:00:00Z
review text: The paper proves that the maximal order type of the wqo of linear orders of finite Hausdorff rank under embeddability is \(\phi_2(0)\), the first fixed point of the \(\varepsilon\)-function. Moreover, it proves that Fraïssé's conjecture restricted to linear orders of finite Hausdorff rank is provable in \(\text{ACA}^+_0\) + ``\(\varphi_2(0)\) is well-ordered'' and, over \(\text{RCA}^+_0\), implies \(\text{ACA}'_0\) + ``\(\varphi_2(0)\) is well-ordered''.
reviewed by: Josef Berger
Mathematics Subject Classification ID: 03B30
Mathematics Subject Classification ID: 03F35
Mathematics Subject Classification ID: 06A07
Mathematics Subject Classification ID: 03D80
zbMATH DE Number: 5620643
zbMATH Keywords: reverse mathematics
zbMATH Keywords: Fraïssé's conjecture
zbMATH Keywords: Hausdorff rank
zbMATH Keywords: maximal order type
MaRDI profile type: Publication
full work available at URL: j.apal.2009.01.007
OpenAlex ID: W2101320428
Wikidata QID: Q122926065
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DOI: 10.1016/J.APAL.2009.01.007
description: scientific article; zbMATH DE number 5620643