Automorphism groups in general
From Peano's Parlour
Rigid models
A model $M$ is rigid if ${\rm Aut}(M)$ is trivial -- that is, its only automorphism is the identity function. Every model of PA has a rigid elementary end extension. (See [1] for a proof of this and much more.)
Question: Does every nonstandard model of PA have a rigid cofinal extension?
