If I understand what you do correctly, the severity classes are just the set differences Vα∖⋃β<αVβ, where {Vα}α∈I is the filtration. I think that you also assume that the quotient Vα/⋃β<αVβ is one-dimensional and equipped with a choice of “positive” direction.
Yes! This is all true. I thought set differences of infinite unions and quotients would only make the post less accessible for non-mathematicians though. I also don’t see a natural way to define the filtration without already having defined the severity classes.
If I understand what you do correctly, the severity classes are just the set differences Vα∖⋃β<αVβ, where {Vα}α∈I is the filtration. I think that you also assume that the quotient Vα/⋃β<αVβ is one-dimensional and equipped with a choice of “positive” direction.
Yes! This is all true. I thought set differences of infinite unions and quotients would only make the post less accessible for non-mathematicians though. I also don’t see a natural way to define the filtration without already having defined the severity classes.