We prove a classification theorem of the “Glimm-Effros” type for Borel order relations: a Borel partial order on the reals either is Borel linearizable or includes a copy of a certain Borel partial order which is not Borel linearizable.
@article{bwmeta1.element.bwnjournal-article-fmv155i3p293bwm,
author = {K\'aroly Simon and Boris Solomyak},
title = {Correlation dimension for self-similar Cantor sets with overlaps},
journal = {Fundamenta Mathematicae},
volume = {158},
year = {1998},
pages = {293-300},
zbl = {0897.28005},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-fmv155i3p293bwm}
}
Simon, Károly; Solomyak, Boris. Correlation dimension for self-similar Cantor sets with overlaps. Fundamenta Mathematicae, Tome 158 (1998) pp. 293-300. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-fmv155i3p293bwm/
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[00001] [2] L. A. Harrington, D. Marker and S. Shelah, Borel orderings, Trans. Amer. Math. Soc. 310 (1988), 293-302.