Constructing Sequences One Step at a Time
نویسنده
چکیده
We propose a new method for constructing Turing ideals satisfying principles of reverse mathematics below the Chain-Antichain Principle (CAC). Using this method, we are able to prove several new separations in the presence of Weak König’s Lemma (WKL), including showing that CAC ` WKL does not imply the thin set theorem for pairs, and that the principle “the product of well-quasi-orders is a wellquasi-order” is strictly between CAC and the Ascending/Descending Sequences principle, even in the presence of WKL.
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In this paper, the kernels (that is the sets of sequences transformed into a constant sequence) of the sequence transformations where each step is obtained from the previous one are studied in detail. It is rst proved that the kernel of each step contains the kernel of the previous step. Then, a technique for constructing the diierence equation satissed by the sequences of the kernel is given. ...
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