I am trying to define an embedding whose range includes classes. Is there a coherent way of assigning "cardinality" to proper classes?

Among the important classes to consider are those Boolean algebras which name generic extensions. In other words, those classes of the universe which reflect the multiverse.

I am trying to define an embedding whose range includes classes. Is there a coherent way of assigning "cardinality" to proper classes?

I am trying to define an embedding whose range includes classes. Is there a coherent way of assigning "cardinality" to proper classes?

Among the important classes to consider are those Boolean algebras which name generic extensions. In other words, those classes of the universe which reflect the multiverse.

I am trying to define an embedding whose range includes classes. Is there a coherent way of assigning "cardinality" to proper classes?

Among the important classes to consider are those Boolean algebras which name generic extensions. In other words, those classes of the universe which reflect the multiverse.

Set Theorists,

Is there ever a reason to assign a cardinality to a proper class? If so, is there a way to do this? Or is it just accepted that classes do not have cardinality, as in if there was a survey question that asks "What is your cardinality?" the sets would mark their cardinality and classes would mark "n/a"?

I am currently reading about Hausdorff gaps in Jech and while this is not part of the reading, the question arose while I was learning.

I am trying to define an embedding whose range includes classes. Is there a coherent way of assigning "cardinality" to proper classes?

Among the important classes to consider are those Boolean algebras which name generic extensions. In other words, those classes of the universe which reflect the multiverse.