Simbologia e modi di dire in inglese

[Luke1984]

I would like to know if there is an equivalent in Italian for a term which appears on this page:

http://www.apronus.com/provenmath/induction.htm

In the proof of the Recursion Principle there is the definition of "proper collection".
I repeat it here in a more readable way (I hope):

$(X,E)$ is a well ordered set
$Y$ is a set
for every $x inX$ let be $I(x) := {yinX:yEx and ynex}$
$D := { j inP(XxY) :$ exists $ x inX $ such that $j$ is a function from $I(x)$ to $Y }$
$g: D->Y$
$A subset X$
$f: A->Y$

$(A,f)$ is a proper collection if and only if:
1) $A$ is an initial segment of $X$
2) for every $x inA$, $f(x)=g(f bigcap (I(x) times Y))$

Maybe this is just a term used only here, to make the proof clearer.
I just wondered if someone had ever known a name for a "thing" like that in italian...

[elgiovo]

Secondo voi quanto è importante conoscere tali termini?

Talking 'bout me? Well, if I had to explain an argument of complex analysis to somebody italian, he wouldn't understand the meaning of "branch point". (and this happened to me)