(EXTRA)ORDINARY EQUIVALENCES WITH THE ASCENDING/DESCENDING SEQUENCE PRINCIPLE

نویسندگان

چکیده

Abstract We analyze the axiomatic strength of following theorem due to Rival and Sands [28] in style reverse mathematics. Every infinite partial order P finite width contains an chain C such that every element is either comparable with no or infinitely many elements . Our main results are following. The Rival–Sands for orders arbitrary equivalent $\mathsf {I}\Sigma ^0_{2} + \mathsf {ADS}$ over {RCA}_0$ For each fixed $k \geq 3$ , $\leq \!k$ decomposable into union two chains {SADS}$ Here denotes recursive comprehension system, ^0_{2}$ $\Sigma ^0_2$ induction scheme, ascending/descending sequence principle, stable principle. To best our knowledge, these versions first examples theorems from general mathematics literature whose exactly characterized by Furthermore, we give a new purely combinatorial result extending do not have antichains, show this extension arithmetical

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ژورنال

عنوان ژورنال: Journal of Symbolic Logic

سال: 2022

ISSN: ['1943-5886', '0022-4812']

DOI: https://doi.org/10.1017/jsl.2022.92