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On the quasi-ordering of Borel linear orders under embeddability

Published online by Cambridge University Press:  12 March 2014

Alain Louveau  and
Jean Saint-Raymond
Alain Louveau
Affiliation:
Équipe D'Analyse, Université Paris-VI, 75252 Paris, France
Jean Saint-Raymond
Affiliation:
Équipe D'Analyse, Université Paris-VI, 75252 Paris, France
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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 Rω, with the lexicographic ordering. For Borel orders embeddable in R2, our proof works in ZFC, but it uses projective determinacy for Borel orders embeddable in some Rn, n < ω, and hyperprojective determinacy for the general case.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 55 , Issue 2 , June 1990 , pp. 537 - 560
Copyright
Copyright © Association for Symbolic Logic 1990

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References

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