Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
8904318 | Annals of Pure and Applied Logic | 2018 | 29 Pages |
Abstract
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 1â of the fragment Î 11-CA0 of second order number theory, or equivalently the set theory KPâ0. 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 1â. We expect that our approach will facilitate analysis of more powerful systems of patterns.
Related Topics
Physical Sciences and Engineering
Mathematics
Logic
Authors
Gunnar Wilken,