FOM: Goedel Collected Works

[Charles Parsons]

Some comments on Alasdair's posting by an editor.

>In reply to Thomas Foster's query, there
>are currently three volumes of the Collected Works.
>The preface to the third volume (1995) says that
>there will be a fourth volume with a selection of
>his correspondence together with a full inventory of
>his Nachlass.

This is correct. It's likely that the additional volume will become two, so
that although it is a selection it is quite extensive.

>
>I believe there were originally plans to publish some of
>the material in the Gabelsberger shorthand notebooks,
>but the preface to Volume III does not mention this.

That is also correct, but some years ago we decided that we would not try
to produce an edition of material from the notebooks. A microfilm of all
the Goedel papers is now on deposit at the Firestone Library of Princeton
University.

>This is understandable but also a little disappointing to
>me as I have always been curious as to how far Goedel
>got with the independence of AC and CH from set theory.
>I've asked various people connected with the project about
>this over the years, and I have had conflicting answers --
>the published literature on this question is not helpful, though
>Goedel himself made quite strong claims in the 1981 JSL article
>by Hao Wang that is a kind of "authorised summary" of his
>scientific career.
>

Probably Goedel's most considered statements on what he accomplished on the
independence questions are in letters to Alonzo Church (1966) and Wolfgang
Rautenberg (1967). These correspondences will appear in our volumes.
(Church and Goedel corresponded at other times on other matters as well.)
What Goedel wrote to Church is (in edited form) incorporated in Church's
paper on Cohen's work in the proceedings of the 1966 International Congress
of Mathematicians. Most of the letter to Rautenberg is translated in volume
II of the Works, p. 159. The claim made to Church is a little more
cautious, possibly because he knew that it would be reflected in Church's
publication. (The latter is quoted on the page preceding the one cited.)

Wang's article should probably be viewed cautiously, although Goedel did go
over at least the first version of it.

Some time ago the editors gave a draft transcription of the notebook
material on the independence of AC to some leading set theorists, who were
unable to determine exactly what Goedel had in mind or what he had in fact
accomplished.

Charles Parsons