I'm presently working in a non-ZF set theory, where there are proper classes. (Think MK or VNBG.) And I'm interested in how to think about the possibility (or impossibility) of proper classes with cardinalities which are in some sense different. (So in this set theory we drop the von Neumann assumption, on which every proper class has the same cardinality.) Can someone point me to resources where people talk about this? I'm familiar w at least a slice of the relevant standard resources in math and phil math - MK's discussion, Parsons' discussion, Maddy's, etc. - but I've been having trouble tracking down discussions of this particular question.

Gratefully in advance,

Anon

I'm presently working in a non-ZF set theory, where there are proper classes. (Think MK or VNBG.) And I'm interested in how to think about the possibility (or impossibility) of proper classes with cardinalities which are in some sense different. (So in this set theory we drop the von Neumann assumption, on which every proper class has the same cardinality.) Can someone point me to resources where people talk about this? I'm familiar with at least a slice of the relevant standard resources in math and phil math - MK's discussion, Parsons' discussion, Maddy's, etc. - but I've been having trouble tracking down discussions of this particular question.

Gratefully in advance,

Anon

I'm presently working in a non-ZF set theory, where there are proper classes. (Think MK or VNBG.) And I'm interested in how to think about the possibility (or impossibility) of proper classes with cardinalities which are in some sense different. (So in this set theory we drop the von Neumann assumption, on which every proper class has the same cardinality.) Can someone point me to resources where people talk about this? I'm familiar w the standard resources in math and phil math - MK's discussion, Parsons' discussion, Maddy's, etc. - but I've been having trouble tracking down discussions of this particular question.

Gratefully in advance,

Anon

I'm presently working in a non-ZF set theory, where there are proper classes. (Think MK or VNBG.) And I'm interested in how to think about the possibility (or impossibility) of proper classes with cardinalities which are in some sense different. (So in this set theory we drop the von Neumann assumption, on which every proper class has the same cardinality.) Can someone point me to resources where people talk about this? I'm familiar w at least a slice of the relevant standard resources in math and phil math - MK's discussion, Parsons' discussion, Maddy's, etc. - but I've been having trouble tracking down discussions of this particular question.

Gratefully in advance,

Anon