A Saturated Model of an Unsuperstable Theory of Cardinality greater than its theory has the Small Index Property

@article{Melles1993ASM,
  title={A Saturated Model of an Unsuperstable Theory of Cardinality greater than its theory has the Small Index Property},
  author={Garvin Melles and S. Shelah},
  journal={Proceedings of The London Mathematical Society},
  year={1993},
  pages={449-463}
}
A model M of cardinality lambda is said to have the small index property if for every G subseteq Aut(M) such that [Aut(M):G] Th(M), then M^* has the small index property. 
2 Citations
AUTOMORPHISM GROUPS OF SATURATED MODELS OF PEANO ARITHMETIC
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By the previous theorem 2. By 1. and [Sh 430, 6.3] 3. If T is stable in λ, then λ = λ <κr(T ) , so if κ r (T ) > ℵ 0 we can let κ from the previous theorem be the least κ such that λ < λ κ
  • By the previous theorem 2. By 1. and [Sh 430, 6.3] 3. If T is stable in λ, then λ = λ <κr(T ) , so if κ r (T ) > ℵ 0 we can let κ from the previous theorem be the least κ such that λ < λ κ
For some strong limit cardinal µ, cf µ = ℵ 0 and µ < λ < 2 µ
  • For some strong limit cardinal µ, cf µ = ℵ 0 and µ < λ < 2 µ
If T is stable in A, then A = A <Kr(r) , so if K r (T) > K o , we can let K from the previous theorem be the least K
  • If T is stable in A, then A = A <Kr(r) , so if K r (T) > K o , we can let K from the previous theorem be the least K
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