The maximal linear extension theorem in second order arithmetic

Authors:
Alberto Marcone;Richard A. Shore
Affiliations:
Dipartimento di Matematica e Informatica, Università di Udine, Udine, Italy 33100;Department of Mathematics, Cornell University, Ithaca, USA 14853
Venue:
Archive for Mathematical Logic
Year:
2011

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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.