Comments on: Math logic reading list (updated)

By: Peter Smith

Peter Smith — Thu, 08 Oct 2009 19:58:10 +0000

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.

By: tomtom

tomtom — Thu, 08 Oct 2009 17:18:40 +0000

The revised list seems to have disappeared from the site. Can anybody help? Tom

By: Peter Smith

Peter Smith — Thu, 10 Sep 2009 11:38:43 +0000

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!

By: Anonymous

Anonymous — Thu, 10 Sep 2009 09:46:29 +0000

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.

By: Simon Hewitt

Simon Hewitt — Wed, 09 Sep 2009 13:14:56 +0000

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

By: Carl

Carl — Tue, 08 Sep 2009 21:08:04 +0000

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.