I’ve spent the last couple of days reorganizing and rewriting the reading list for the Part II Math Logic paper (that’s a third year undergraduate paper for philosophers). It was a rather minimalist affair, and I’ve taken a step or two towards its becoming an annotated study guide.
The paper is something of a Cambridge institution, pretty much unchanged in its basic syllabus since when I took it a long time ago. It rather distinctively mixes an introduction to the “greatest hits” as far as formal results are concerned, with a look at some of the philosophical issues arising.
Anyway, having had some initial comments here and from local grad students, you can now download my third shot at an updated list. All comments and suggestions for further improvement (within the current, fixed, syllabus) will still be very welcome.
Thanks for reminding me it was a temporary link: I've put a link to the final-for-now version on the Faculty's website.
The revised list seems to have disappeared from the site. Can anybody help? Tom
Carl> Thanks — in particular for the Ferreirós reference: I've added a short historical aside to the reading list, and suggested reading that paper. (I've added a reference to the Kanamori piece too.)
Simon> I didn't know the Rayo/Yablo piece. Is interesting and I've added it too.
Anon> Yes, I like the Just/Weese book too, and on second thoughts I agree it is worth adding a mention of this. Thanks!
It's easy to make a massive list of books on set theory, but I found Just and Weese's "Discovering Modern Set Theory: Vol. 1, the Basics", American Mathematical Society, an excellent introduction to the subject, and is possibly worth a mention.
http://books.google.co.uk/books?id=TPvHr7fcvHoC&printsec=frontcover&source=gbs_navlinks_s#v=onepage&q=&f=false
The book is very well written, (even funny in places), nicely typeset, with plenty of examples and exercises, and has chapters devoted to the AoC, etc.
There's also a second volume, with much more advanced material.
The Vaananen paper is actually on-line as a PDF:
http://tiny.cc/MMfz9
Rayo and Yablo's 'Nomialism through De-nominalization' is an interesting contribution to the debate around SOL, plural quantification and natural language:
Agustin Rayo and Stephen Yablo, "Nominalism Through De-Nominalization", Noûs 35 (2001), pp. 74-92
The list you've made is an impressive collection of material for a student to digest. Here are a few extra papers from the BSL that might be useful for their historical remarks or for mining additional references.
* van Dalen and Ebbinghaus, "Zermelo and the Skolem paradox", Bull. Symbolic Logic 6 (2000), no. 2, 145–161.
* Ferreirós, "The road to modern logic—an interpretation", Bull. Symbolic Logic 7 (2001), no. 4, 441–484.
* Kanamori, Akihiro, "The mathematical development of set theory from Cantor to Cohen", Bull. Symbolic Logic 2 (1996), no. 1, 1–71.
I assume that constructive and intuitionistic mathematics is outside the scope of the list.
A side note: I noticed that, in the summary, you take the syntactic approach to second-order logic (saying that it allows quantification over predicates) rather than a semantic one. I wish that more were done in the introductory literature to dispel the notion that second-order logic differs from first-order logic primarily in syntax. Nobody is going to come away from Shapiro's book with that idea, however.