Let $p$ be a type over a set $A$ and suppose that $p$ does not fork over $A$.
In proposition 3.39 of http://www.math.ucla.edu/~chernikov/teaching/StabilityTheory285D/StabilityNotes.pdf the following is stated:
"Since $p$ does not fork over $A$ and the set of all $L(\mathbb{M})$ formulas forking over $A$ is an ideal, there is a global $q$ extending $p$ and non-forking over $A$."
I am a little confused by this. The formulas that do not fork over $A$ do form a filter and I know that types can be associated with various ultra-filters. In fact those ideas are used in proposition 3.23 (of the same set of notes). However it is based on the assumption that the type $p$ is finitely satisfiable in $A$. But I'm not sure how to modify this proof to fit the current setting (While the notes are building up to theorems about simple theories, this particular statement is for an arbitrary theory.)
Edit 1: I found a proof that can be adapted to this context in Tent and Ziegler's Model Theory text. But if anyone knows how to make this proof I'd like to see that proof.