On the strength of Fraïssé’s conjecture
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We show that Fraïssé’s conjecture that the class of linear orderings is well-quasiordered under embedability is proof theoretically strong. Indeed, even special cases of its restriction to wellorderings implies ATR0: If the class of wellorderings has no infinite antichains or no infinite descending chains then ATR0. is provable in RCA0. These results answer questions of Clote, Friedman and Hirst.
KeywordsInitial Segment Rank Function Recursive Function Final Segment Recursive Tree
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