On the quasi-ordering of Borel linear orders under embeddability

Publisher： Cambridge University Press

E-ISSN： 1943-5886|55|2|537-560

ISSN： 0022-4812

Source： The Journal of Symbolic Logic, Vol.55, Iss.2, 1990-06, pp. : 537-560

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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 R n , n < ω, and hyperprojective determinacy for the general case.

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