A conjecture about product order and logic
The considerations below were with an error, see the comment. Product order $latex {\prod \mathfrak{A}}&fg=000000$ of posets $latex {\mathfrak{A}_i}&fg=000000$ (for $latex {i \in n}&fg=000000$ where $latex {n}&fg=000000$ is some index subset) is defined by the formula $latex {a \leq b \Leftrightarrow \forall i \in n : a_i \leq b_i}&fg=000000$. (By the way, it is a […]
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 […]