Definition 2

Let M be a model of T and an infinite set I be an indiscernible sequence in M. A complete theory T has the (M,I)-Isolation Property iff for any special (N,J) first-order equivalent to (M,I), for any pseudo-finite subset A of J in N, any finite subset C of N, and any element a of N, there is a countable A0⊆A such that
tp(a/(A0∪ C)) isolates tp(a/(A∪ C)) in N.

Theorem 3

The (M,I)-Isolation Property implies the (M,I)-Pseudo-finite Homogeneity Property.

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