Reference Request Scott's Trick Does anyone know of a reference for Scott's Trick. I can't find it in Set Theory-Jech?
 A: Scott's trick is explained in Thomas Forster's book:

Thomas Forster, Logic, Induction and Sets. Cambridge University Press, 2003

In particular, Section 8.6 is of interest regarding Scott's trick.

The trick itself is not difficult. The universe is based on a cumulative hierarchy, $V_\alpha$ and we can assign ranks to a set: the rank of $x$ is the least ordinal $\alpha$ such that $x\in V_{\alpha+1}$.
Now given any definable class (e.g. "all the sets equipotent with $x$") Scott's trick suggests that we take only those of minimal rank in the class. This is a set because it's a definable subset of a particular $V_\alpha$.
Note that this makes a very heavy use of the axiom of regularity.
A: Indeed it is included in Jech's book, but it is not attributed to Scott. This is from Set Theory, The Third Millennium Edition, revised and expanded, page 65:

Given a class $C$, let
  $$ (6.4)\qquad\qquad \hat C = \{x \in C : (\forall z \in C)\ \text{rank}\:x \leq \text{rank}\: z\}.  $$
  $\hat C$ is always a set, and if $C$ is nonempty, then $\hat C$ is nonempty. Moreover, (6.4) can be applied uniformly.

After that, some examples and consequences are given. This is what's commonly known as Scott's trick.
