The maximal linear extension theorem in second order arithmetic

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.

18 pages. New proof of the maximal chain theorem in ATR_0

Cited by in corpus (6)

• Finding descending sequences through ill-founded linear orders
• Reverse Mathematics and initial intervals
• Linear extensions of partial orders and Reverse Mathematics
• Reverse mathematics, well-quasi-orders, and Noetherian spaces
• (Extra)ordinary equivalences with the ascending/descending sequence principle
• Computing Maximal Chains