[FOM] questions re Axiom of Choice

Andreas Blass ablass at umich.edu
Mon Feb 25 13:14:45 EST 2019

I believe the relevant paper of Pincus is

Pincus, David
Cardinal representatives.
Israel J. Math. 18 (1974), 321–344.

Andreas Blass

Date: Sat, 23 Feb 2019 20:53:14 -0800
From: Mitchell Spector <spector at alum.mit.edu>
To: Paul Blain Levy <p.b.levy at cs.bham.ac.uk>,   Foundations of
        Mathematics <fom at cs.nyu.edu>
Subject: Re: [FOM] questions re Axiom of Choice
Message-ID: <eff5956e-bf64-fe95-c1c2-974b43e9b696 at alum.mit.edu>
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This statement is equivalent to: "Every set of Scott cardinals has a
choice function."

According to Asaf Karagila's answer at
https://math.stackexchange.com/q/423369 , Jech and Sochor
showed that this is not provable in ZF, and then Pincus gave another
proof of this fact.  I don't
have specific references though.


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