On Fraïssé’s conjecture for linear orders of finite Hausdorff rank

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Annals of Pure and Applied Logic 160 (3):355-367 (2009)
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Abstract

We prove that the maximal order type of the wqo of linear orders of finite Hausdorff rank under embeddability is φ2, the first fixed point of the ε-function. We then show that Fraïssé’s conjecture restricted to linear orders of finite Hausdorff rank is provable in +“φ2 is well-ordered” and, over , implies +“φ2 is well-ordered”

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10.1016/j.apal.2009.01.007

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Citations of this work

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Proof-theoretic investigations on Kruskal's theorem.Michael Rathjen & Andreas Weiermann - 1993 - Annals of Pure and Applied Logic 60 (1):49-88.
Ordinal numbers and the Hilbert basis theorem.Stephen G. Simpson - 1988 - Journal of Symbolic Logic 53 (3):961-974.
On the equimorphism types of linear orderings.Antonio Montalbán - 2007 - Bulletin of Symbolic Logic 13 (1):71-99.

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