Fwd: Davis's honor roll

Martin Davis martin.david.davis at gmail.com
Mon Jun 28 18:39:35 EDT 2021

It's clear from the forwarded message below that I was unfair to Rosser.

---------- Forwarded message ---------
From: Grant Olney Passmore <grant.passmore at cl.cam.ac.uk>
Date: Sun, Jun 27, 2021 at 7:22 AM
Subject: Re: Davis's honor roll
To: Martin Davis <martin at eipye.com>

Yes, interesting! BTW in case it got lost in the shuffle, I paste below a
bit of info on the first edition chapter of Rosser's book, which seems to
quite deliberately separate out and only assume countable choice:

Here is an online browsable edition from 1953, which I believe is the first

The Axiom of Choice is covered in Ch XIV, with the following contents:
1. The General Axiom of Choice
2. How Indispensable is the Axiom of Choice?
3. The Denumerable Axiom of Choice

In 1, he explores various formulations / equivalents of 'full Choice', but
as far as I can tell, he does not officially 'add' any axiom of choice to
his system until p512 (in the section of Denumerable Choice) where he says:

``Consequently, we shall assume the denumerable axiom of choice as one of
our axioms''
and defines `Axiom Scheme 15' as `AxC(Den)'.

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