[I posted this back in August: and I’m moving this to the front of the blog to invite more contributions/suggestions!]

I haven’t looked at all at the Teach Yourself Logic Study Guide since the 2015 version came out on January 1st. I earlier had it in mind to do a mid-year update in time for the new (northern hemisphere) academic year: but that bird has long flown. The main Guide continues to be downloaded eighty or more times a month. It certainly seems to serve some need, and I get appreciative emails. So I will put time aside over the coming months to get a 2016 version ready for next January 1st.

So now’s the time for feedback on both style and content. As far as style goes, while keeping to the spirit of the present Guide, what would make it more user-friendly? Should I keep the one-big-PDF format, or go over to a suite of webpages? [Added: after thinking a bit, I continue to incline strongly to the PDF format — it is easier to maintain, but also easier to read off line, and for students to work with by highlighting, commenting, etc. onscreen. But thoughts on style/layout etc. are still very welcome.]

As to content, any suggestions for additions, improvements? One thing I’ll want to say something about is The Open Logic project [added: I’ve posted some thoughts that recently] But are there more conventional new(ish) publications, or overlooked older publications, that could definitely rate a recommendation for student use?

Feedback from logicians at any stage of their career, whether taking first steps or on their zimmer frame, will be most welcome — either in the comments below, or by email (address at the bottom of my “about” page here).

Doug SpoonwoodDoes the list contain any reference to any texts which talk about extended propositional calculi with functorial variables or propositional calculi with quantifiers? If not, you might want to include a reference to Arthur Prior’s book Formal Logic. The book also has other virtues such as having a sizeable index of axiom sets for logical calculi.

DJ SidleI’d love to hear what you think about Smullyan’s recent book “A Beginner’s Guide to Mathematical Logic.” From the table of contents, it seems to cover most of what a 1st course in the subject should touch on and Smullyan typically writes clearly and concisely with wonderful examples.

Rowsety MoidI’ve just noticed that the 2nd edition of Leary’s Friendly Introduction to Mathematical Logic is out now in paperback and at a reasonable price.

This resolves something that’s always bugged me a bit about the Guide: that the Friendly Introduction was so highly recommended but was expensive and out of print.

Peter SmithI was looking only a couple of months ago to see if the promised second edition had appeared, and was disappointed not to find it. So this is good to know. Thanks!

Daniil FruminHave you considering mentioning formal semantics in the guide?

L.T.F. Gamut’s “Logic, Language and Meaning” Vol 2. touches both upon basic type theory and formal semantics.

Daniel NagaseHmm, something that could be useful in the model theory section is an algebra text for logicians (instead of a logic text for algebraists). A lot of model theory involves, say, algebraically closed fields, so it’d be nice to have a good reference for learning this stuff. If it also included a bit of algebraic geometry (so one can eventually understand what the Mordell-Lang conjecture is about), that would be very helpful.

Also, perhaps you could add in the beginning a few words about the consequence relation. I say this because there are two consequence relations floating around, so to speak, one that internalizes the variable assignments and another that doesn’t, and they can lead to different results when you’re considering formulas (Jeffrey Ketland has a blog post about this over at M-Phi — it’s also an exercise in the first chapter of Doets book on model theory). Most books that I’ve seen work with an “external” variable assignment, but maybe it’s a good idea to warn the reader to look out for this distinction (I’ve met a few people who were confused by this).

Peter SmithThanks for this. Do you have any suggestions yourself for an algebra text that you’ve found helpful?

Daniel NagaseSorry for the delay. I was actually hoping that you would have some indications yourself! =)

Anyway, for universal algebra, I found Mal’cev’s book on

Algebraic Systemsto be helpful, though the notation can take some time to get used to (Grätzer’s book is another contender, but I found it too encyclopedic some times). For algebra in general, I’ve been toying with Paolo Aluffi’sAlgebra: Chapter 0, which seems more self-contained than most algebra books I’ve come across. The only problem is that, at 700 pages, it’s a bit daunting if you’re just looking for something to fill in the gaps for doing model theory.Daniel NagaseI’ve been trying a variety of other abstract algebra books and I found two more that could be helpful: Hungerford’s

Abstract AlgebraandAlgebra. The former is especially good if you’re a beginner (like me!) who needs a bit more detail than usual with some proofs. It also contains a nice review of the structure of the integers, including modular arithmetic, which is always useful when doing (say) group theory. The latter is more of a reference book, and it does require a bit more maturity to work with, but it includes almost anything a (beginning?) model theorist will need to know (especially on fields). Both books are wonderfully organized, with clear indications about what each chapter and section will cover and also which theorems from which chapter/section are used to prove what. This is tremendously useful if you’re planning on reading the book just for specific references, instead of reading it from cover to cover.Peter SmithMany thanks for these suggestions! I’m fond of Paolo Aluffi’s

Algebra: Chapter 0, but I’ll take a look at these in the library.Rowsety MoidI like having a PDF for the main part of the guide, supplemented by web pages for some particular areas and books (pretty much the arrangement you have now).

Re type theory, this book might be of interest:

Peter B. Andrews, An Introduction to Mathematical Logic and Type Theory: To Truth Through Proof.

Unfortunately, it’s absurdly expensive — £108 on Amazon, even for a paperback.

BTW (and I may have mentioned this somewhere else), the 6th edition of Mendelson’s Introduction to Mathematical Logic is out, and the consistency proof that was an appendix to the first edition has been restored. (Unfortunately, in the current printing, the script letters are extremely faint throughout the book.)

AlexSecond-order and higher-order logics and their semantics would be a very worthwhile addition, I reckon. Also maybe some pointers on category theory (your own notes?), type theory, and HoTT (the HoTT Book?).

Peter Smith§4.4.1 does say something about second-order logic and its semantics.

And there is a link in the Guide to my category theory page here.

But I agree that there should be something more about type theory.