@article{oai:oist.repo.nii.ac.jp:00000453,
 author = {Wilken, Gunnar},
 issue = {1},
 journal = {Annals of Pure and Applied Logic},
 month = {Sep},
 note = {We provide mutual elementary recursive order isomorphisms between classical  ordinal notations, based on Skolem hulling, and notations from pure elementary  patterns of  resemblance  of  order  2, showing  that the latter characterize the  proof-theoretic ordinal  1∞ of  the fragment  Π1–CA0 of  second  order  number  theory,  orequivalently  the  set  theory  KPA .  As a corollary,  we  prove  that  Carlson’s result on the well-quasi orderedness of respecting forests of order 2 implies transfinite  induction up to the ordinal 1∞. We expect that our approach will facilitate  analysis of  more powerful  systems of patterns.},
 pages = {54--82},
 title = {Pure patterns of order 2},
 volume = {169},
 year = {2017}
}