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Constructing sequences one step at a time

2020; World Scientific; Volume: 20; Issue: 03 Linguagem: Inglês

10.1142/s0219061320500178

1793-6691

Henry Towsner,

Advanced Algebra and Logic

We propose a new method for constructing Turing ideals satisfying principles of reverse mathematics below the Chain–Antichain ([Formula: see text]) Principle. Using this method, we are able to prove several new separations in the presence of Weak König’s Lemma ([Formula: see text]), including showing that [Formula: see text] does not imply the thin set theorem for pairs, and that the principle “the product of well-quasi-orders is a well-quasi-order” is strictly between [Formula: see text] and the Ascending/Descending Sequences principle, even in the presence of [Formula: see text].