We prove that there is no maximum element, under Borel reducibility, in the class of analytic partial orders and in the class of analytic oriented graphs. We also provide a natural jump operator for these two classes.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-fm192-3-3,
author = {Alain Louveau},
title = {Analytic partial orders and oriented graphs},
journal = {Fundamenta Mathematicae},
volume = {189},
year = {2006},
pages = {233-243},
zbl = {1112.03043},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm192-3-3}
}
Alain Louveau. Analytic partial orders and oriented graphs. Fundamenta Mathematicae, Tome 189 (2006) pp. 233-243. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm192-3-3/