Abstract
We show that the maximal linear extension theorem for well partial orders is equivalent over RCA 0 to ATR 0. Analogously, the maximal chain theorem for well partial orders is equivalent to ATR 0 over RCA 0.
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Marcone’s research was partially supported by PRIN of Italy. Part of this work was carried out while Shore was a GNSAGA Visiting Professor at the Department of Mathematics and Computer Science “Roberto Magari” of the University of Siena. He was also partially supported by NSF Grant DMS-0852811 and Grant 13408 from the John Templeton Foundation. We thank Andreas Weiermann for some useful bibliographic references. We thank the anonymous referee for pointing out an error in an earlier version of the proof of Theorem 6.4.
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Marcone, A., Shore, R.A. The maximal linear extension theorem in second order arithmetic. Arch. Math. Logic 50, 543–564 (2011). https://doi.org/10.1007/s00153-011-0231-1
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DOI: https://doi.org/10.1007/s00153-011-0231-1