On Fraïssé’s conjecture for linear orders of finite Hausdorff rank |
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| Authors: | Alberto Marcone,Antonio Montalb n |
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| Affiliation: | aDipartimento di Matematica e Informatica, Università di Udine, viale delle Scienze 206, 33100 Udine, Italy;bDepartment of Mathematics, University of Chicago, Chicago, IL 60637, USA |
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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(0), 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(0) is well-ordered” and, over  , implies  +“φ2(0) is well-ordered”. |
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| Keywords: | Reverse mathematics Fraï ssé ’ s conjecture Hausdorff rank Maximal order type |
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