Difference between revisions of "Automorphism groups in general"

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(Created page with "== 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 ...")
 
 
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A model $M$ is '''rigid''' if ${\rm Aut}(M)$ is trivial -- that is, its only automorphism  
 
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.  
 
is the identity function. Every model of PA has a rigid elementary end extension.  
(See <cite> schmerl2002:automorphisms </cite> for a proof of this and much more.)
+
(See <cite> schmerl2002:automorphism </cite> for a proof of this and much more.)
  
 
Question: Does every nonstandard model of PA have a rigid cofinal extension?
 
Question: Does every nonstandard model of PA have a rigid cofinal extension?

Latest revision as of 08:54, 7 February 2013

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?