Avigad on Mathematical Logic and Computation

A heads up, as they say. Jeremy Avigad’s new book Mathematical Logic and Computation has now been published by CUP (or at least, an e-version is already available on the Cambridge Core system if you have access — with the hardback due soon). Here’s a link to the front matter of the book, which gives you the Table of Contents and the Preface. Between them, they give you a fair idea of the coverage of the book.

As you’d expect from this author, this book is very worth having, an excellent addition to the literature, with plenty more than enough divergences and side-steps from the more well-trodden paths through the material to be consistently interesting. Having quickly read a few chapters, and dipped into a few more, I’d say that the treatments of topics, though very clear, are often rather on the challenging side (Avigad’s Carnegie Mellon gets very high-flying students in this area!). For example, the chapters on FOL would probably be best tackled by someone who has already done a course based on something like Enderton’s classic text. But that’s not a complaint, just an indication of the level of approach.

When the physical version becomes available — so much easier to navigate! — I’m going to enjoy settling down to a careful read through, and maybe will comment in more detail here. Meanwhile, this is most certainly a book to make sure your library gets.

4 thoughts on “Avigad on Mathematical Logic and Computation”

  1. This has become annoying. The book was going to be out at the end of October: now it’s 24 November.

    I find books being announced months before they’re available almost as irritating as the ridiculously high prices.

  2. I find myself wondering what the “As you’d expect from this author” is about, since I don’t think I’ve heard of him (if I have, I don’t remember), and when I looked him up, nothing stood out as “that must be it”.

    I might not like this book. Algebraic semantics, what looks like quite a bit of proof theory, type theory, the emphasis on syntax (even “our goal is to use semantics to illuminate syntax rather than the other way around”) — I see those as warning signs. Still, though those aren’t things I like, they’re things I’d like to see explained clearly; it’s possible this book will do that. And it may have other virtues.

    Since £59.99 is not quite ridiculously expensive, I’ll try to get a copy. However, Amazon UK won’t let me preorder it, for some reason. It says “Sorry, this item can’t be sent to your selected address” (even though it’s the address I use all the time without any problem). Strange.

    1. Well, Jeremy Avigad is pretty well known for his stuff on proof theory, ordinal analysis, etc. — and more recently his work on the Lean project. Maybe not so much your cup of tea!

      It could be that printed copies the book are available in the US; but it hasn’t appeared in the CUP bookshop here yet.

      1. Thanks for “ordinal analysis” as a clue. That’s the part of proof theory that does interest me, and adding it to the search turns up some interesting stuff such as this paper, Ordinal Analysis Without Proofs.

        Ordinal analysis isn’t mentioned on his CMU home page, however, on the Wikipedia page about him, or in any other place where I looked.

        On the pre-ordering problem, I should clarify that I am in the UK, trying to order from Amazon UK, and using my usual UK address that Amazon UK has happily sent books to for years. It’s not a major problem, though, just behaviour strange enough that I wanted to mention it.

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