Generalizations of free set, thin set, and rainbow Ramsey theorems to barriers are proved, with computability bounds and reverse mathematics results.
Simpson,Subsystems of second order arithmetic, second ed., Perspectives in Logic, Cambridge University Press, Cambridge; Association for Symbolic Logic, Poughkeepsie, NY
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Free sets, thin sets and rainbows for barriers
Generalizations of free set, thin set, and rainbow Ramsey theorems to barriers are proved, with computability bounds and reverse mathematics results.