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/