On the logical strength of Nash-Williams' theorem on transfinite sequences
Logic
2009-09-25 v1
Abstract
We show that Nash-Williams' theorem asserting that the countable transfinite sequences of elements of a better-quasi-ordering ordered by embeddability form a better-quasi-ordering is provable in the subsystem of second order arithmetic Pi^1_1-CA_0 but is not equivalent to Pi^1_1-CA_0. We obtain some partial results towards the proof of this theorem in the weaker subsystem ATR_0 and we show that the minimality lemmas typical of wqo and bqo theory imply Pi^1_1-CA_0 and hence cannot be used in such a proof.
Keywords
Cite
@article{arxiv.math/9408204,
title = {On the logical strength of Nash-Williams' theorem on transfinite sequences},
author = {Alberto Marcone},
journal= {arXiv preprint arXiv:math/9408204},
year = {2009}
}