On page 307 of Vaught's paper "Denumerable models of complete theories", theorem 2.1.2 states that there is a denumerable model $\frak{A}$ of $T$ such that if, for each $j\in \omega, \:P\_j$ is a non-principal prime ideal (now called ultrafilter) of $F\_{p\_j+1}(T)$, then there is a denumerable model $\frak{A}$ of $T$ such that $P\_0(\mathfrak{A}), P\_1(\mathfrak{A}), \cdots$ are all empty. Then Vaught said that 2.1.2 was proved by Ehrenfeucht.


I wonder which of Ehrenfeucht's papers contains theorem 2.1.2.



Question in Vaught's paper
The Omitting Types Theorem has its roots in the independent work of Leon Henkin and Steven Orey in the early 1950’s on $\omega$-logic. This line of work was advanced further by Andrzej Grzegorczyk, Andrzej Mostowski, and Czeslaw Ryll-Nardzewski, where a more explicit version of the theorem can be found. The form of the theorem we have used is apparently due to Andrzej Ehrenfeucht around 1955 —- Ehrenfeucht never published his version.  

[source](https://people.math.sc.edu/mcnulty/762/modeltheory.pdf)


