(EXTRA)ORDINARY EQUIVALENCES WITH THE ASCENDING/DESCENDING SEQUENCE PRINCIPLE
(EXTRA)ORDINARY EQUIVALENCES WITH THE ASCENDING/DESCENDING SEQUENCE PRINCIPLE
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升序/降序原则的（额外）普通等价
DOI：
10.1017/jsl.2022.92
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发表时间：
2022
期刊：
影响因子：
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通讯作者：
FIORI-CARONES M
中科院分区：
文献类型：
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作者：
FIORI-CARONES M
我们以逆向数学的方式分析了 Rival 和 Sands [28] 给出的以下定理的公理强度。每个有限宽度的无限偏序 P 都包含一个无限链 C，使得 P 的每个元素都可以与 C 的任何元素进行比较，或者可以与 C 的无限多个元素进行比较。我们的主要结果如下。任意有限宽度的无限偏序的 Rival-Sands 定理等价于 。
We analyze the axiomatic strength of the following theorem due to Rival and Sands [28] in the style of reverse mathematics. Every infinite partial order P of finite width contains an infinite chain C such that every element of P is either comparable with no element of C or with infinitely many elements of C. Our main results are the following. The Rival–Sands theorem for infinite partial orders of arbitrary finite width is equivalent to .