[FOM] Question about B-sets

[Paul B Levy]

Hi,

This question is about ZF- meaning ZF with neither Foundation nor Choice.

Let's say that a "B-set" is a set that is equinumerous with a
well-founded set.

Coret's Axiom B says that every set is a B-set.  This follows from
Choice, from Foundation and from Antifoundation.  We're not assuming
Axiom B, so there might be (for example) a set that consists of a vast
number of distinct Quine atoms and is not a B-set.

Question: is the property of being a B-set universe-independent?  That
is, if U is a Grothendieck universe, and X is a B-set in U, must X be
equinumerous with a well-founded set in U?

Paul



-- 
Paul Blain Levy
School of Computer Science, University of Birmingham
http://www.cs.bham.ac.uk/~pbl