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:
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It was an error.