On the quasi-ordering of borel linear orders under embeddability

Journal of Symbolic Logic 55 (2):537-560 (1990)
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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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A Wadge hierarchy for second countable spaces.Yann Pequignot - 2015 - Archive for Mathematical Logic 54 (5):659-683.
Borel quasi-orderings in subsystems of second-order arithmetic.Alberto Marcone - 1991 - Annals of Pure and Applied Logic 54 (3):265-291.
A multiplication operation for the hierarchy of norms.Alexander C. Block & Benedikt Löwe - 2018 - Annals of Pure and Applied Logic 169 (7):656-673.

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On the determinacy of games on ordinals.L. A. Harrington - 1981 - Annals of Mathematical Logic 20 (2):109.

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