A theorem from Rival and Sands and reverse mathematics

Abstract: In 1980 Ivan Rival and Bill Sands proved that for each infinite poset P with finite width (i.e. such that there is a fixed finite bound on the size of antichains in P) there is an infinite chain C ⊆ P such that each element of P is comparable to none or to infinitely many elements of C. Moreover, if P is countable, C can be found such that each element of P is comparable to none or to cofinitely many elements of C. We prove that some versions of the previous theorem are equivalent to the Ascending/descending sequence principle or to related known principles of the reverse mathematics zoo. (Joint work with Alberto Marcone, Paul Shafer and Giovanni Soldà)

logic

Audience: researchers in the topic

Computability theory and applications

Series comments: Description: Computability theory, logic

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