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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 extension of M, and if Y⊆M is coded in N, then (M,Y)≢(M,X)?
The answer is `yes' is either (M,X)⊭\SPA or \Th(M,X)∉\SSy(M).