Back to the Study Guide?

I’m almost done with the category theory book — at least as far as the draft content is concerned. There will be tinkering to be done (in particular with respect to having a consistent line on issues of “size”), and then there will be the joys of proof-reading and indexing. But I’m beginning to think occasionally about the next logical project — a second edition of the much-downloaded Study Guide. In particular, I’ll want to rethink the early chapters introducing FOL and then making revising suggestions. So what new books have been published over the last few years whose coverage of FOL (and entry-level model theory, in so far as that is distinct) might be usefully recommended?

David Marker (the author of that modern classic Model Theory: An Introduction) has just published An Invitation to Mathematical Logic covering FOL, some model theory, some computability theory, and making connections with other areas of mathematics. At a quick first look, it is indeed a graduate-level book, not so much an invitation to newbies as something to tackle after entry-level texts.

The next book is by Ieke Moerdijk and Jaap van Oosten (who I think of as category theorists). Sets, Models and Proofs was published at the end of 2018, and I’m not sure how I missed it before. It is undergraduate-friendly and very short, only 130 pages before the end matter. And yes, it talks about sets and models before proofs. But, again at a first browse, this looks useful

Dag Westerståhl published his Foundations of Logic: Completeness, Incompleteness, Computability at the beginning of this year. Evidently a retirement project, based on a long teaching history. I’ve read some with enjoyment, and I do like the tone a lot. I think that at least parts of this could well be entry-level recommendations. So high on my list of readings for when I seriously get down to revising the Study Guide.

One more book for now. Three Views of Logic by Donald W. Loveland, Richard Hodel and S.G. Sterrett came out a dozen years ago, but was recently recommended to me. And this looks interesting, and again I’m not sure how I overlooked this. The first 90 pages are on FOL, but done with a resolution proof-system (and this could be an entry-level recommendation on this approach). The next 130 pages are on computability by Richard Hodel (whose Mathematical Logic is rightly very highly regarded).

Then the last part of the book, perhaps misleadingly entitled “Philosophical Logic” is about non-classical logics, particularly for relevance systems. Not my cup of tea, but looks well done.

So there’s some homework for me, to fill idle hours, taking more careful looks at these books. But what else have I missed, of recent — or perhaps not-so-recent — books, particularly on FOL,  that could be worth recommending in the Guide?

I don’t trust the absolute download stats, but relative numbers must be reliable. As I’ve said before, the Guide is by far the most downloaded of the Big Red Logic Books (as many times a month as IFL and IGT together), and the number of downloads increases over time. And to my continuing surprise, it actually sells about 600 paperbacks a year too. So it must be worth putting in the effort to update/improve it. And, sad to relate, I do rather enjoy working on it …

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