Difference between revisions of "Automorphism groups in general"
From Peano's Parlour
(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: | + | (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 07:54, 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?
