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.

Classification theory and the number of isomorphic models, revised

Studies in Logic and the foundations of Math

1990

Classification theory and the number of isomorphic models, revised, Studies in Logic and the foundations of

Mathematics

1990

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