[FOM] References on continuum hypothesis in non-well-founded set theory

[Andrej Bauer]

I have been contacted by an amateur who came up with what he claims to 
be a model of non-well-founded set theory in which the continuum 
hypothesis is false.

As I am not an expert in this field, I would very much appreciate some 
references about this subject. His particular model seems _not_ to 
satisfy replacement, foundation and separation. This means that it would 
be useful to have references to works discussing what happens with 
continuum hypothesis when various standard axioms are missing (not just
foundation).

I thank you in advance for your help. I will post a summary of the 
references you send me.

Best regards,

Andrej