The set of ideals on an infinite join-semilattice is a boolean algebra

The below is wrong, because pointfree funcoids between boolean algebras are not the same as 2-staroids between boolean algebras. It was an error.

I have just discovered that the set of ideals on an infinite join-semilattice is a boolean algebra (moreover it is a complete atomistic boolean algebra).

For me, it is a very counter-intuitive theorem (after all the set of ideals “should” not be boolean algebra, except of the finite case). Is it worth to call it a paradox?

See this link for details:
http://math.stackexchange.com/questions/1475328/when-ideals-are-a-boolean-algebra