Abstract:The paper is devoted to a reverse-mathematical study of some well-known consequences of Ramsey's theorem for pairs, focused on the chain-antichain principle CAC, the ascending-descending sequence principle ADS, and the Cohesive Ramsey Theorem for pairs CRT 2 2 . We study these principles over the base theory RCA * 0 , which is weaker than the usual base theory RCA0 considered in reverse mathematics in that it allows only ∆ 0 1 -induction as opposed to Σ 0 1 -induction. In RCA * 0 , it may happen that an unboun… Show more
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