On the quasi-ordering of borel linear orders under embeddability

Journal of Symbolic Logic 55 (2):537-560 (1990)

Abstract

We provide partial answers to the following problem: Is the class of Borel linear orders well-quasi-ordered under embeddability? We show that it is indeed the case for those Borel orders which are embeddable in R ω , with the lexicographic ordering. For Borel orders embeddable in R 2 , our proof works in ZFC, but it uses projective determinacy for Borel orders embeddable in some $\mathbf{R}^n, n , and hyperprojective determinacy for the general case

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References found in this work

On the Determinacy of Games on Ordinals.L. A. Harrington - 1981 - Annals of Mathematical Logic 20 (2):109.

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A Wadge Hierarchy for Second Countable Spaces.Yann Pequignot - 2015 - Archive for Mathematical Logic 54 (5-6):659-683.
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