Weaker cousins of Ramsey's theorem over a weak base theory

The paper is devoted to a reverse-mathematical study of some well-known consequences Ramsey's theorem for pairs, focused on the chain-antichain principle CAC, ascending-descending sequence ADS, and Cohesive Ramsey Theorem pairs CRT22. We these principles over base theory RCA0⁎, which weaker than usual RCA0 considered in reverse mathematics that it allows only Δ10-induction as opposed Σ10-induction. In may happen an unbounded subset N not bijective correspondence with N. Accordingly, Ramsey-theoretic split into at least two variants, “normal” “long”, depending sense set witnessing required be infinite. prove normal versions our principles, like colours, are equivalent their relativizations proper Σ10-definable cuts. Because this, they all Π30- but Π11-conservative and, any model RCA0⁎+¬RCA0, if true then computably relative set. long exhibit one behaviours: either imply RCA0⁎ or Π30-conservative RCA0⁎. conservation results obtained using variant so-called grouping principle. also show cohesive COH, strengthening CRT22, never consequence, does follow from RT22