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If I'm not mistaken, it was in his seminal paper “An Essentially Undecidable Axiom System”, published in

Proceedings of the International Congress of Mathematicians (1950), 1952:729–730,

where R.M. Robinson proved that Gödel Incompleteness Theorem still applies to Peano Axioms if we drop the induction schema (hence showing that infinite axiomatization is not necessary for essential undecidability), in what we now call Robinson Arithmetic.

I would like to know:

  • Is actually this paper what I should be looking for?
  • Can it be found anywhere on the net? (I already tried on MathSciNet, SpringerLink, JSTOR and Google Scholar, without success)
  • Can anyone pinpoint to closely related, or at least similar, accessible papers?

(Note: I already have the book "Undecidable theories", which he published in collaboration with Tarski, but I'd prefer to locate papers about 'Robinson theory', specifically).

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    $\begingroup$ Two related papers are - Jones & Shepherdson, Variants of Robinson's essentially undecidable theory ${\rm R}$. MR0710365 - Vaught, On a theorem of Cobham concerning undecidable theories, MR0156788 $\endgroup$
    – François G. Dorais
    Commented Jul 5, 2010 at 20:24
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    $\begingroup$ All the ICM Proceedings can now be found, and searched, at mathunion.org/ICM $\endgroup$
    – John Stillwell
    Commented Sep 15, 2010 at 21:11
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    $\begingroup$ All the proceedings of the ICMs: mathunion.org/ICM $\endgroup$
    – Felipe Voloch
    Commented Sep 15, 2010 at 21:12
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    $\begingroup$ One can easily find the cited work via the links given by John Stillwell and Felipe Voloch. However, it is only a one-page abstract. It seems that contributed papers were not actually printed in the Proceedings? $\endgroup$
    – Nate Eldredge
    Commented Sep 15, 2010 at 21:37
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    $\begingroup$ @AndersLundstedt No, just the summary published in the ICM proceedings, but it is very informative. You can find it at page 737 of this pdf: mathunion.org/fileadmin/ICM/Proceedings/ICM1950.1/… $\endgroup$
    – Jose Brox
    Commented Jan 14, 2022 at 17:53

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Hi Jose, it's in the British library collection: http://snurl.com/z16ud Haven't checked what the fees are, but you could order it from there.

Alternatively, you could try the LMS: http://www.lms.ac.uk A good chance they will have the procs in their library, and you can get photocopies for a nominal fee.

Several other similar alternatives too.

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  • $\begingroup$ Thanks Bob! But I'd like to find it 'online' (i.e., in electronic format), if possible (if not, I will resort to your nice suggestions!) $\endgroup$
    – Jose Brox
    Commented Jul 5, 2010 at 23:31
  • $\begingroup$ Oh, on a closer inspection I see that the British Library offers the option of sending an electronic copy, but the fee is indeed a bit high (over 8 pounds). I'd like to get free access to the article from my University, if possible. $\endgroup$
    – Jose Brox
    Commented Jul 5, 2010 at 23:36
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    $\begingroup$ I know this is not a discussion blog , I make it short : How disgraceful it is to have to pay for work that was done with our taxes!! $\endgroup$
    – Jérôme JEAN-CHARLES
    Commented Oct 3, 2010 at 1:30
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    $\begingroup$ As of 2023, good full-text pdf’s of all past ICM proceedings are available from the IMU website at mathunion.org/icm/proceedings The abstract cited in the question is in Vol I of the 1950 proceedings, near the end; as noted in comments on question, it’s a 1-page abstract, not a full paper, but it is very clear and self-contained. $\endgroup$
    – Peter LeFanu Lumsdaine
    Commented Nov 23, 2023 at 15:09

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