Difference between revisions of "Saturated models"

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In a recent paper Nurkhaidarov and  Schmerl 2011 proved the following: Let κ be regular, uncounale, and such that κ<κ=κ. For each completion TPA let  MκT be the saturated model of T of cardinality κ. There is a set T of completions of PA, such that |T|=20 and for all T,TT, if TT, then Aut(MκT)Aut(MκT). The following question is left open: Are there T and T such that TT and Aut(MκT)Aut(MκT)?
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In a recent paper Nurkhaidarov and  Schmerl 2011 proved the following: Let κ be regular, uncountable, and such that κ<κ=κ. For each completion TPA let  MκT be the saturated model of T of cardinality κ. There is a set T of completions of PA, such that |T|=20 and for all T,TT, if TT, then Aut(MκT)Aut(MκT). The following question is left open: Are there T and T such that TT and Aut(MκT)Aut(MκT)?

Revision as of 17:09, 17 January 2013

The automorphism group

In a recent paper Nurkhaidarov and Schmerl 2011 proved the following: Let κ be regular, uncountable, and such that κ<κ=κ. For each completion TPA let MκT be the saturated model of T of cardinality κ. There is a set T of completions of PA, such that |T|=20 and for all T,TT, if TT, then Aut(MκT)Aut(MκT). The following question is left open: Are there T and T such that TT and Aut(MκT)Aut(MκT)?