Is the empty set internal?

Question

Is the empty set internal or not?

And is there a proof (either way), or is it just a convention? If it's just a convention, why was that particular convention chosen?

Answer 1

The answer given in the comments can be simplified. Every finite set is internal. In particular, so is the empty set. Moreover the empty set is standard because it is already contained in the standard universe before a nonstandard enlargement is defined. Recall that all standard things are internal but not vice versa. For example, an infinitesimal number is an internal object but obviously it is not standard.