Difference between revisions of "Omitting theories of undefinable sets"

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(Created page with "Suppose $M$ is countable recursively saturated and $X$ is an undefinable subset of $M$. Is there a countable recursively saturated $N$ such that $N$ is an elementary end exten...")
 
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Suppose $M$  is  countable recursively saturated and
 
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$X$ is an undefinable subset of $M$. Is there a countable recursively saturated  $N$ such that $N$ is an elementary end extension of $M$,
 
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and if $Y \subseteq M$ is coded in $N$, then $(M,Y) \not\equiv
 
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(M,X)$?
 
  
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The answer if `yes' is either $(M,X)\not\models PA^*$ or ${\rm Th}(M,X)\notin {\rm SSy}(M)$.
 
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This problem is listed in Kossak, Roman; Schmerl, James H.
 
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The structure of models of Peano arithmetic.
 
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Oxford Logic Guides, 50. Oxford Science Publications. The Clarendon Press, Oxford University Press, Oxford, 2006. xiv+311, but, unfortunately, with many typos.
 

Latest revision as of 09:08, 18 January 2013

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