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].

中文翻译：

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一步一步构建序列

我们提出了一种构建图灵理想的新方法，该方法满足链-反链（[公式：见正文]）原理下的逆向数学原理。使用这种方法，我们能够证明存在 Weak König 引理（[公式：参见文本]）的几个新分离，包括证明 [公式：参见文本] 并不意味着对的薄集定理，并且原理“良准阶的乘积是良准阶”严格介于[公式：见正文]和升序/降序原理之间，即使存在[公式：见正文]。