How are 'primitive recursive' sets defined? The following is taken from Inner Models and Large Cardinals by Martin Zeman (beginning of chapter 2).
Let $\kappa$ be an ordinal. $U \subseteq \mathcal P(\kappa)$ is suitable iff 


*

*$\kappa$ is primitive recursively closed and

*If $A_1, \ldots, A_n \in U$, $\nu_1, \ldots, \nu_m \in \kappa$ and $B$ is primitive recursive in the predicates $A_1, \ldots, A_n$ and the parameters $\nu_1, \ldots, \nu_m$, then $B \cap \kappa \in U$.


While it isn't defined by the author, I'm fairly certain that "$\kappa$ being primitive recursively closed" means that for every $\alpha_1, \ldots, \alpha_n < \kappa$ and every primitive recursive ordinal function $f(x_1, \ldots, x_n)$ we have that $f(\alpha_1, \ldots, \alpha_n) < \kappa$. 
Question 1 Am I right about being a primitive recursively closed ordinal?
I'm less certain that I understand property 2. What does $B$ being primitive recursive in the predicates $A_1, \ldots, A_n$ and parameters $\nu_1, \ldots, \nu_m$ mean? I guess it means the following:
There is a primitive recursive set function $f(x_0, x_1, \ldots, x_n, y_1, \ldots, y_m)$ such that $B = \{x \mid f(x,A_1, \ldots, A_n, \nu_1, \ldots, \nu_m) \neq \emptyset \}$. (In general $B$ is then a proper class, but that doesn't concern me, since I'm only interested in $B \cap \kappa$ anyways.)
Question 2 Is this the definition Martin Zeman had in mind?

edit: Should anyone in the future stumble upon this question: There is now a typed script by Jensen on Fine Structure available on Ronald Jensen's website or Ralf Schindler's website. It's still under early development and will be extended and corrected. Right now the relevant information can be found on page 19ff.
 A: There is a good chance that these primitive recursive functions come from the fine structure setting and are the same as those defined in Jensen's notes: http://www.mathematik.hu-berlin.de/~raesch/org/jensen/pdf/AS_2.pdf
Let $\bar{x} = (x_1, ..., x_n)$. It is the smallest class generated by the following schemes:
(1) For each $i$, the projection function is primitive recursive: $p_i(\bar{x}) = x_i$.
(2) The pairing function. Let $i,j < n$, then $\mathrm{pair}_{i,j}(\bar{x}) = \{x_i, x_j\}$. 
(3) Composition: Suppose $h : V^k \rightarrow V$, and $g_1, ..., g_k : V^n \rightarrow V$ are primitive recursive functions, then $f(\bar{x}) = h(g_1(\bar{x}), ..., g_k(\bar{x}))$ is a primitive recursive function. 
(4) Suppose $g(\bar{x}, y)$ is a primitive recursive function, then so is $f(\bar{x},y) = \bigcup_{z \in y} g(\bar{x},z)$. 
(5) Primitive recursion: Suppose $g(\bar{x}, y, v)$ is primitive recursive, then so is $f(\bar{x},y) = g(\bar{x}, y, \langle f(\bar{x},z) : z \in y\rangle)$. 

A set $A$ is primitive recursive closed if for all $f$ primitive recursive and all $\bar{x}$ which are tuples from $A$, $f(\bar{x}) \in A$. 
