[FOM] Question about B-sets

Paul B Levy P.B.Levy at cs.bham.ac.uk
Wed Oct 24 12:44:23 EDT 2018


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 Blain Levy
School of Computer Science, University of Birmingham

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