What does the uppercase greek symbol pi mean for sets?

Question

What operation is denoted in e.g.:

$\Pi_{i \in I} S_i$

The document in question is:

John C. Reynolds - Types, abstraction, and parametric polymorphism

Since no index order is specified, the operation must be commutative and associative.

I am thinking that is means intersection, based on the idea that union is like addition, and intersection like multiplication. But I want to confirm it.

Thanks.

Answer 1

It usually stands for the cartesian product of the $S_i$, that is the set \[ \prod_{i\in I} S_i = \left\{f \colon I \to \bigcup_{i\in I} S_i \biggm| f(i) \in S_i \text{ for all } i \in I\right\} \]