Saturated models

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The automorphism group

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 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|=20 and for all T,TT, if TT, then \aut(MκT)\aut(MκT).