Just / Weese contains the following theorem (p 126):
Theorem 5: Let $\mathbf Z \neq \varnothing$ and let $\mathbf W \subseteq \mathbf Z \times \mathbf Z$ be a wellfounded set-like class. Let $\mathbf G$ be a functional class such that $dom(\mathbf G)$ consists of all pairs of the form $\langle f,z \rangle$, where $z \in \mathbf Z$ and $f$ is a function with domain $I_{\mathbf W}(z)$. Then there exists exactly one functional class $\mathbf F : ]\mathbf Z \to \mathbf V$ such that $ \mathbf F (z) = \mathbf G ( \mathbf F \mid I_{\mathbf W} (z), z) \hspace{0.5 cm} \forall z \in \mathbf Z$
On the same page before the theorem they write "...In Chapter 12 we shall see that the existence of a definable, set-like wellorder of the universe is relatively consistent with $ZFC$. ..."
I am not aware of any other places in the book where the word "set-like" is used, in particular not a definition of what it means. Could someone give me the definition of "set-like" class and explain to me what it means? Many thanks for your help.