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In the first edition of Elliott Mendelson's classic Introduction to Mathematical Logic (1964) there is an appendix, giving a version of Schütte's (1951) variation on Gentzen's proof of the consistency of PA. This is intriguing stuff, crisply and quite accessibly presented. The appendix is, however, suppressed in later editions (in fact, from the second onwards, I learn from the comments below).

Now, a number of people have said that the appendix is one of the most interesting things about the book. I agree. I too remember being quite excited by it when I first came across the book a long time ago!

So: has anyone heard a folkloric story about why Mendelson suppressed the appendix? I've never heard it suggested that there is a problem with the consistency proof as given.

Context, if you are interested: I'm writing up a survey of some of the Big Books on Mathematical Logic that will become part of my Teach-Yourself-Logic Guide, and I've got to Mendelson. You can get the current version of the Guide by going to

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No appendix in the 2nd edition (1979). The preface doesn't mention this change. Excerpt: This new edition contains considerable improvements over the first edition. Much new material has been added. [...] Completely new is a section at the end of the book, Answers to Selected Exercises, which should improve the usefulness of the book as a textbook as well as for independent study. With all these changes, I have attempted to preserve the spirit of the original book, which was intended to be a simple, clear introduction to mathematical logic unencumbered by excessive notation and terminology. – Martin Jan 27 '13 at 15:37
Thanks, Martin! (I have the 1964 and 1997 editions on my shelves.) "Curiouser and curiouser!" cried Alice. – Peter Smith Jan 27 '13 at 15:55
I’ve only ever seen the 1964 edition; some initial segment of it was the text for the introductory undergraduate logic course that I took in the late 1960s. Consequently, I’ve no sense of how the later editions changed. My very tentative guess, however, would be that perhaps he felt that having to introduce a Gentzen-style formalism before getting to the proof proper was just a bit too much, at least for an appendix, especially if he was adding a substantial amount to the body of the text. – Brian M. Scott Jan 27 '13 at 21:15
@Brian Maybe it is indeed as simple as you say. And yes, Mendelson 64 came out just two years before I took the Math Logic paper in tripos, and got me through! I owe the book a lot. – Peter Smith Jan 27 '13 at 22:11
The question has now been posted on MathOverflow: – Zev Chonoles Feb 12 '13 at 17:22
up vote 6 down vote accepted

Answering my own question (but some might be interested!) ...

Before posting this question I did search around a bit (probably inefficiently and certainly quite ineffectively) to see if I could find an email for Elliott Mendelson to ask him directly! But anyway, he picked up my similar query on FOM and very kindly wrote to me:

I was intrigued by your comments about the consistency proof of PA that appeared in the First Edition of my logic book. I omitted it in later editions because I felt that the topic needed a much more thorough treatment than what I had given, a treatment that would require more space than would be appropriate in an introduction to mathematical logic.

I can understand that. Though I think the pointers he gave in that Appendix did spur on quite a few readers to find out more, so I still think it was a Very Good Thing, and it was perhaps a pity to drop it.

[Prof. Mendelson has kindly allowed me to quote him.]

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