Abstract
We prove Menger’s theorem for countable graphs in \({{\Pi^1_1\tt{-CA}_0}}\). Our proof in fact proves a stronger statement, which we call extended Menger’s theorem, that is equivalent to \({{\Pi^1_1\tt{-CA}_0}}\) over \({{\tt{RCA}_0}}\).
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This research was partially supported by NSF grants DMS-0554855 and DMS-0852811.
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Shafer, P. Menger’s theorem in \({{\Pi^1_1\tt{-CA}_0}}\) . Arch. Math. Logic 51, 407–423 (2012). https://doi.org/10.1007/s00153-012-0269-8
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DOI: https://doi.org/10.1007/s00153-012-0269-8