On the logical strength of the automorphism groups of free nilpotent groups

2011/12/11 by Tolstykh, Vladimir
#03C60 (Primary) 20F19 #20F28 (Secondary) #FOS: Mathematics #Group Theory (math.GR) #Logic (math.LO)

paper · doi:10.48550/arxiv.1112.2369

Abstract

Considering a particular case of a problem posed by Saharon Shelah, we prove that the automorphism group of an infinitely generated free nilpotent group N first-order interprets the full second-order theory of the set rank(N) in the empty language.

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