I’m interleaving two projects at the moment, spending time on one or the other as the mood takes me. One project is to update the messy draft notes Category Theory II. The other is to revise and improve the Beginning Mathematical Logic Study Guide.
The Guide gives topic-by-topic recommendations for reading on various areas of math logic. Early versions had an Appendix which also looked, book-by-book, at some of the Big Texts that covered more than one area. That Appendix has stayed online, but has been left untouched for the better part of a decade. Yet it gets downloaded pretty steadily, about a fifth as often as the main Guide (so between three and four hundred times a month, if we can believe the stats counter, which I don’t).
At long last, there’s a new version of the Appendix, now in the same format as the Guide. I’ve updated the entry on Ebbinghaus, Flum and Thomas, and added entries on Mileti and Avigad (basically from the blog posts here). I’ll be adding/revising more over the coming three months or so as I do more (re)reading as background homework for revising the Guide.
What other good books published in, say, the last twenty years and not yet mentioned in the Appendix should I take another look at? Rautenberg, for sure. Kaye’s The Mathematics of Logic and Kunen’s The Foundations of Mathematics are certainly worth a revisit. But what other suggestions of wider ranging, near-entry-level books are there?
It’s not yet published, but Buss’s in-progress Introduction to Mathematical Logic looks very nice. Available here: https://tinyurl.com/7y39y6xr
I noted that you don’t have a book note on Boolos, Jeffrey, and Burgess! Maybe it would be worth adding one, perhaps explaining also the main differences between the 3rd and the 5th editions? Speaking of older books, why not add also entries for Smullyan’s First-Order Logic (and maybe his newer books as well) and Suppes’s Introduction to Logic?
Another is Yu. I. Manin and B. Zilber, A Course in Mathematical Logic for Mathematicians (2010, a revision with new chapters of Manin’s 1977 book).
The preface describes the changes and is visible in the preview of the Kindle edition on Amazon UK. The first part of one of the new chapters is a category-theoretic view of computation.
Yes, in particular, to Manin’s book: I have a copy and if I recall right thought it full of interesting things when I dipped in some time ago …. I’ve a lot of (enjoyable?!?) homework ahead ….
I just came across Boolos’s rather negative review of the first edition in Journal of Symbolic Logic. In brief, Boolos thought that Manin was quite inconsistent about the audience he seemed to be writing to and, as a result, that the book was unsuitable for use as a textbook.
I’d be interested in hearing how much less applicable this criticism is to the second edition than the first.
Here is a very positive review (of the 2nd ed):
https://www.maa.org/press/maa-reviews/a-course-in-mathematical-logic-for-mathematicians
I don’t know but how about Bell & Machover? Though it’s an old textbook including many topics in one volume, not your kind of book I think…
Michael L. O’Leary, A First Course in Mathematical Logic and Set Theory (2016)
Ernst-Erich Doberkat, Special Topics in Mathematics for Computer Scientists: Sets, Categories, Topologies and Measures (2015)
Laszlo Csirmaz and Zalán Gyenis, Mathematical Logic: Exercises and Solutions (Problem Books in Mathematics) (2022)
Peter J. Cameron, Sets, Logic and Categories (1998)
Haimanti Sarbadhikari and Shashi Mohan Srivastava, A Course on Basic Model Theory
Daniel Cunningham, Mathematical Logic: An Introduction (2023) — just published
Yves Nievergelt, Logic, Mathematics, and Computer Science: Modern Foundations with Practical Applications (2nd ed, 2015)
Daniele Mundici, Logic: a Brief Course (2012)
Ieke Moerdijk and Jaap van Oosten, Sets, Models and Proofs (2018)