Difference between revisions of "Saturated models"
From Peano's Parlour
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− | In a recent paper Nurkhaidarov and Schmerl 2011 proved the following: Let κ be regular, | + | 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 T⊇PA let MκT be the saturated model of T of cardinality κ. There is a set T of completions of PA, such that |T|=2ℵ0 and for all T,T′∈T, if T≠T′, then Aut(MκT)≇Aut(MκT′). The following question is left open: Are there T and T′ such that T≠T′ 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 T⊇PA let MκT be the saturated model of T of cardinality κ. There is a set T of completions of PA, such that |T|=2ℵ0 and for all T,T′∈T, if T≠T′, then Aut(MκT)≇Aut(MκT′). The following question is left open: Are there T and T′ such that T≠T′ and Aut(MκT)≅Aut(MκT′)?