Short version: there is at last, after three years, an updated version of the TYL Guide. Click on the cover picture for links!

Long version: The title gives it away! — this is an annotated guide to logic books and other resources suitable for self-study, starting a step up from ‘baby logic’ and going though to quite advanced stuff. It is a PDF, now over 90 pp., formatted for onscreen reading, with a lot of live links.

The TYL page is the most visited page here on this site (with 70K visits last year), with the Guide getting thousands more visits too at its academia.edu location. So there is evidently more than enough interest in the Guide to make it well worthwhile maintaining it, and trying to improve it.

This new version is a ‘maintenance upgrade’. Its overall structure has been clarified by dividing it into three parts, some entries have been revised, and a few new recommendations added. But there are no new sections, and I haven’t found myself wanting to change many main recommendations this time. Have any stand-out books been published in the last three or four years which really ought to have shot to top of any reading list? As always, comments and suggestions are most welcome.

Daniel NagaseA couple of quick comments:

(1) There is a new edition of Steinhart’s

More Precisely, which includes new chapters on information theory and game theory. I think it is also worth mentioning that there is a companion website with exercises for each chapter: https://sites.broadviewpress.com/moreprecisely/(2) On model theory, I was surprised that you didn’t mention Jonathan Kirby’s new book, which I learned about from this website! I found it very clear and engaging, not to mention modern. Also, John Baldwin’s

Model Theory and the Philosophy of Mathematical Practiceshould perhaps be mentioned… Button & Walsh are concerned with applying model-theoretic tools to philosophical problems, whereas Baldwin is more concerned with applying philosophy to model theory, so they are in a sense complementary books (though Button & Walsh is much more clear and organized).(3) I was very surprised to note that you don’t mention Levy’s

Basic Set Theoryin the guide. Sure, it is terse and more advanced, but it is also extremely rigorous and has some very nice observations about key points; indeed, it is my “go to” book when I need to check set-theoretical facts that don’t involve forcing or large cardinals.(4) You mention that vol. 2 of Girard’s

Proof Theory and Logical Complexitywas not published, but he has since made it available in his website: https://girard.perso.math.cnrs.fr/Accueil.html (scroll to the very bottom of the page).(5) AMS’s “Student Mathematical Library” has recently released three books that may be of interest: Katz & Reimann’s

An Introduction to Ramsey Theory, which has a whole chapter on connections with logic (including incompleteness, indiscernibles, and Paris-Harrington), Murty & Fodden’sHilbert’s Tenth Problem, and Hils & Loeser’sA First Journey through Logic. I can’t comment on the last one, but the first two seem to be pretty good.(6) Finally, if you could somehow manage to mention Smoryński’s

Logical Number Theory, I think it would be a very nice addition… he is a very good writer and I found that a superb book.Peter SmithMany thanks for this! Very briefly, forgetting about Kirby was a senior moment (OK, from now on need to start more systematic note-keeping for future updates!). Baldwin’s book, however, I think is unrecommendable. It’s a while since I looked at Levy, but yes it is clear and good (but I’ll need to check how it compares). Hmmm: I thought I had a copy of Smoryński — where has it gone?! Thanks for the other suggestions!

Peter SmithMany thanks again for these very helpful comments/reminders!

(1) I’ve updated the entry for

More Precisely.(2) Forgetting about Kirby’s book was a senior moment: I’ve now added a not-very-positive entry about it. And a negative remark too about Baldwin’s book.

(3) I agree about Levy’s book. It was a mistake to let it fall between the cracks as too advanced in approach for the “entry-level” section, but not going far enough into higher-level material like large cardinals and forcing to feature in Ch. 8. It now gets an appropriate mention at the beginning of the latter chapter.

(4) Thanks for the reference which I hadn’t noticed!

(5) I’ll check out the first two of these. The third I have taken a quick look at, and frankly it does seem to be a quite unnecessary addition to the literature, being too quick to be useful.

(6) I agree. I enjoy Smoryński’s idiosyncratic style. Added.

Rowsety MoidI haven’t been able to find anything about Baldwin’s book in the latest TYL guide, not even by using Preview’s search facility on the pdf.

Peter SmithOops … I know at one point I did write a brief para: but somehow it didn’t get saved (I can’t find it in the version history). Odd. I’ve added another brief para to the intended effect. Thanks for catching that! (I just hope that there aren’t other unsaved intended corrections/additions).