2025/01/17 by Boissonneau, Blaise, De Mase, Anna, Jahnke, Franziska +1
#03C60 #03C64 #06F20 (Primary) #12J20 #12L12 (Secondary) #FOS: Mathematics #Group Theory (math.GR) #Logic (math.LO)
paper · doi:10.48550/arxiv.2501.10531
We show that every non-trivial ordered abelian group G is augmentable by infinite elements, i.e., we have G\preccurlyeq H⊕ G for some non-trivial ordered abelian group H. As an application, we show that when k is a field of characteristic 0, then k is not t-henselian if and only if all henselian valuations with residue field k are (∅-)definable.