Actual Infinity in Reality?

[SteveII]

You are answering a metaphysical question with a mathematical axiomatically-driven abstraction. Mathematical axiomatically-driven abstractions are not part of the pool where logic goes for information. By the definition of the terms, you have not *shown* anything to be logical.

You really can't mean that. Mathematics (and certainly NOT metaphysics) is the prototypical logical subject.

I clearly said "Mathematical axiomatically-driven abstractions" are not sources of logic. The noun in that phrase is abstractions not mathematics. 

Here is an argument:
1. It is possible that space is flat (in fact, the observed evidence suggests this).
2. Spatially flat manifolds can be infinite in extent. (R^4 is an appropriate example)
3. Hence it is possible that space is infinite in extent.
4. As far as we can see, space is homogeneous (the same at all locations and in all directions)
5. Hence, it is possible that there are an infinite number of stars.

Now, what is you 'metaphysical' issue with either mathematical 'abstractions' or physical possibilities?

That's a mess in addition to not being a valid argument. 5 does not have anything to do with the other 4. At most, 1-4 is trying to argue for infinite space. Stars came out of left field. 

I don't think 3 follows from 1 and 2. In other words, 1 and 2 could be true but that does not give any indication that 3 is true.