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Given an outcome, how to assess its goodness in the partial/total order?
I am looking for different ways to assess an outcome goodness in the given order. By goodness I mean how good this outcome is compared to the other outcomes in the order.
For instance, assume I have ...
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Is there a ring with the lattice of ideals isomorphic to $(\omega+1)^{\operatorname{op}}?$
In this question, I gave an example of a ring whose lattice of two-sided ideals is order-isomorphic to $\omega+1$. I've been playing a bit with trying to find rings with a given lattice of ideals ...
