The metamathematics of Fraïssé's order type conjecture

A well ordering has the property that any non-empty subset has a minimum element. In [Girard (i) ATR0 proves that the collection S n of countable scattered linear orderings at level n of the Hausdorff hierarchy is better quasi ordered (bqo), and (ii) ATR0 proves that "if α is an ordinal and Q is bqo then Q α is bqo".

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