On the logical strength of Nash-Williams' theorem on transfinite sequences
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 Pi11-CA0 but is not equivalent to Pi11-CA0. We obtain some partial results towards the proof of this theorem in the weaker subsystem ATR0 and we show that the minimality lemmas typical of wqo and bqo theory imply Pi11-CA0 and hence cannot be used in such a proof.
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