The author computes the Kleinberg sequences derived from the three different normal ultrafilters on δ₃¹.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-fm171-1-4, author = {Benedikt L\"owe}, title = {Kleinberg sequences and partition cardinals below d51}, journal = {Fundamenta Mathematicae}, volume = {173}, year = {2002}, pages = {69-76}, zbl = {0999.03047}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm171-1-4} }
Benedikt Löwe. Kleinberg sequences and partition cardinals below δ₅¹. Fundamenta Mathematicae, Tome 173 (2002) pp. 69-76. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm171-1-4/