[FOM] Question about B-sets
Paul B Levy
P.B.Levy at cs.bham.ac.uk
Wed Oct 24 12:44:23 EDT 2018
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
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