Year: 2021

Pavel Haas Quartet and Boris Giltburg, video recording for the Library of Congress

Now available: wonderful new video performances recorded at the Suk Hall in Prague, of Smetana’s String Quartet no. 2 in D minor, Bartók’s String Quartet no. 4, and Brahms, Piano Quintet in F minor, op. 34. The Brahms in particular was a revelation to me — with Boris Giltburg’s playing quite magical. (He is also responsible for some striking photos of the quartet’s new line-up.)

The PHQ sounding so good too with their very impressive new violist Luosha Fang. It is difficult indeed to believe that they had been rehearsing together only a few weeks when this was filmed. A whole series of live concerts are now announced on their updated website  though mostly in the Czech Republic or nearby. But there are two more forthcoming online performances scheduled soon, about which more in a later post.

Website woes (updated again)

For a day, all the comments here on blog posts and on static pages oddly disappeared. But by magic they have now reappeared. By magic, because I spent a couple of hours online with Bluehost without resolving the problem. (I can’t be too cross about that, apart from the annoying waste of time —  Bluehost have been absolutely stars at sorting issues in the past). And now, in some random fiddling on seemingly unrelated aspects of the site, the comments have reappeared. Hey ho.

But still, maybe this is all telling me that — after more than ten years — it is really well past time to update the WordPress theme, and do various other under-the-bonnet updates. I’ve been putting this off for too long. Bluehost have set things up so I can play with a test site for a while before going live. So there’s a project for rainy evenings …

Beginning Mathematical Logic: A Study Guide

I’ve renamed the old Teach Yourself Logic study guide; it is now more aptly called Beginning Mathematical Logic: A Study Guide. And there is now a new version of Part I of the Guide (all 95 pages of it) which you can download from here. It’s taken some time to settle on a style for the expanded Guide (though in the end I have not worried too much about keeping the level of the “overviews” of various topics consistent in level), and also it’s a judgement call where to place e.g. a quick introduction to second-order logic.

If you read the PDF from within a browser (as opposed to downloading it and using a PDF reader) it seems best to use Firefox on a Mac. Because then, if you go back after clicking a link, you are returned to your place in the Guide: Safari returns you unhelpfully to the beginning of the Guide.

All comments/corrections gratefully received as always — but perhaps better to use email until I can sort out the comment handling on the blog. The comments will arrive in my admin dashboard but won’t be visible.

New look, new hardback

The three Big Red Logic Books have a new look. I’m staying with the red theme, but no longer using the free Amazon KDP online cover-builder which produced their rather muddy colour and muddy swirls. The outsides, then, are a bit less dull. I’m afraid the insides of the paperbacks stay just the same!

More importantly, perhaps, a hardback of Gödel Without (Too Many) Tears is published today. It is currently available from e.g. Barnes and Noble (in the US), Gardners (the UK library book suppliers), Booktopia (in Oz), as well as the local Amazons. I hope it will soon propagate to other sellers like Blackwells. It won’t just appear on bookshop shelves, however: you’ll have to order it.

I’m not really expecting anyone reading this blog to buy it for themselves! However, you might like to recommend the hardback to your local friendly university or college librarian. Some librarians are pretty resistant to buying from Amazon (especially self-published paperbacks). That’s why I’m experimenting with hardback publication. We are going a step up here, using the same print-on-demand providers now used e.g. by CUP for some of their books, with a “proper” ISBN officially assigned to the Logic Matters imprint. It is still pretty cheap as academic hardbacks go — £14 in the UK and comparable prices elsewhere (so this isn’t going to make my fortune: to be honest, I’ll be pretty surprised if I even recoup the set-up costs.)

Of course the PDF version is still freely available, and I’ve kept the paperback version as Amazon-only as that absolutely minimizes the price to students. But I like to think that the book should be available on the shelves in university libraries, so please take a moment to recommend the hardback! Its ISBN is 978-1916906303. 

(Apologies by the way to readers down under that the paperback is still not locally printed and hence not cheaply available to you: Amazon say they are working on being able to produce paperbacks in the relevant format “soon” …)

Update: At the moment Amazon UK are giving a very long delivery date for the hardback, but I hope that’s temporary. Amazon US by contrast are giving a relatively short delivery date.


A number of distractions (good distractions!) from logical writing projects recently. For a start, we spent some days near the Suffolk coast, a few miles inland from Aldeburgh. The first time we’ve stayed away from Cambridge in these days of Covid. Initially, we were quite irrationally tentative about doing that — but this seems a quite common reaction after more than a year of restrictions. But we had a great time. The weather was good enough for lots of breezy walks. And being by the sea always very much lifts the spirits.

Back home to hours of nerdy amusement for me, playing around with a new bit of serious software, Affinity Publisher. Extraordinarily inexpensive but powerful alternative to Adobe InDesign. Lots of terrific reviews, and certainly seems quite excellent to me. Have used it to design good-enough covers — still big and red but slightly snappier — for hardback versions of the Big Red Logic Books, and I’ll use the same redesign for the republished paperbacks. More about this when the first hardbacks become available, shortly I hope.

Not least among the distractions, my new 24″ iMac has arrived. Entry-level in blue, since you asked.

Took a day to clear my study into a fit state to have somewhere to put it, and half another day to set it up, transferring files across, installing software and so on. But I’m bowled over by the result.

I’ve not had a desktop machine for well over a decade. So the difference between this and my trusty (but soon-to-be-traded-in) six year old MacBook Pro is wonderful. The big screen in particular is amazing. For LaTeX, being able to work with source code and PDF output side-by-side in big windows is a delight. And LaTeX compiles a large diagram-heavy file about 2.5 times faster too, which is a nice bonus.

The iMac itself is a thing of beauty (significantly better in reality, I’d say, than in the adverts). Even Mrs Logic Matters is impressed. The front-side colour is pleasingly muted. And those “white bezels” which Mac forums were complaining about a lot when the machine was launched in fact strike me as something of a design triumph. They aren’t glaring white — but a sort of slighty-grey off-white and so, in use, the edges of the screen shade off in your peripheral vision into your background wall (at least, if your background wall is fairly neutral like my study wall), in a way which works very well. I could go on. But if you were wavering about whether to get one, I’d say just do it!

Going back and forth

You might have missed Jacob Plotkin’s comment a week ago about about a reference (by me!) to “Cantor’s back-and-forth proof”:

Cantor did not invent/discover or use this method of proof. That honor belongs independently to Felix Hausdorff and E.V. Huntington.

Jacob gave a reference to the short paper where he spells out the evidence. I’ve now had a chance to read it, and it is interesting and instructive (and after all, it is always better to get our history right rather than wrong). So let me add a link to where you can find the paper!

Now’s the time to buy …

For reasons I really won’t bore you with, I need to be republishing my three print-on-demand paperback books, in order to make them more widely available (e.g. in Australia). I’ll also take the opportunity of arranging for — still inexpensive — hardbacks to be published, which will become available through bookstores and library suppliers (with proper ISBNs, etc., to gladden your librarian’s heart). I hope this is all done by mid June.

At the moment you have to use Am*z*n: Intro to Formal Logic is just £8.99/$11; Intro to Gödel’s Theorems is £7.99/$9.99; and Gödel Without (Too Many) Tears is £3.99/$4.99 — with comparable prices in euros. Amazing bargains, of course :) But for reasons I also won’t bore you with, the paperback prices might have to increase a little on re-publishing. So now could be just the time to buy one of the Big Red Logic Books, if you’ve been dithering. Just saying ….

PHQ and Boris Giltburg, radio recording

Boris Giltburg and the Pavel Haas Quartet were playing last night to a live audience at the Louisiana Museum of Modern Art (that’s in Denmark, near Elsinore, on the Øresund coast).

The concert — in which they performed the Brahms and Dvorak Piano Quintets — was broadcast on Danish radio, and the concert is available for listening online on DR P2. (Player at the foot of the page; their concert starts at 43:04). Great stuff!

Roman Kossak’s Model Theory for Beginners

Following on from his Mathematical Logic (2018), Roman Kossak has now published Model Theory for Beginners: 15 Lectures (College Publications, 2021). As the title indicates, the fifteen chapters of this short book — just 138 pages — have their origin in introductory lectures given to graduate students in CUNY. Roughly speaking, the topics of the first half of this new book overlap quite closely with the second half of his previous book. And after grumbling a bit about Part I of that earlier book, I did warm considerably to the model-theoretic Part II, which I think makes for a very approachable elementary introduction to a cluster of issues about definability.

The new treatment is aimed at a rather more sophisticated reader, the writing is a bit less relaxed, and indeed becomes increasingly terse as the book progresses (in later chapters, I could often have done with a sentence or two more motivational chat). But overall, this strikes me as a welcome book. Though I’m at all not sure it is all suitable for beginners.

In a little more detail, after initial chapters on structures and (first-order) languages, Chapters 3 and 4 are on definability and on simple results such as that ordering is not definable in (Z, +). Chapter 5 introduces the notion of types, and e.g. gives Cantor’s back-and-forth proof that countable dense linearly ordered sets without endpoints are isomorphic to (Q, <). Chapter 6 defines elementary equivalence and elementary extension, and establishes the Tarski-Vaught test. Then Chapter 7 proves the compactness theorem, Henkin-style, with Chapter 8 using compactness to establish some results about non-standard models of arithmetic and set theory.

So there is a somewhat different arrangement of initial topics here, compared with books whose first steps in model theory are applications of  compactness. But the early chapters are indeed nicely done. However, I don’t think that Kossak’s Chapter 8 will be found an outstandingly clear and helpful first introduction to applications of compactness — it will probably be best read after e.g. Goldrei’s nice final chapter in his logic text.

Chapter 9 is on categoricity — in particular,  countable categoricity. (Very sensibly, Kossak wants to keep his use of set theory in this book to a minimum; but he does have a section here looking at κ-categoricity for larger cardinals κ.) And now the book starts requiring rather more of its reader. Chapter 10 is on indiscernibility and the Ehrenfeucht-Mostowski Theorem: but it is difficult to get a sense from this chapter of quite why this matters.

Up to this point, the structures we’ve been looking at are all officially relational. Chapter 11 adds functions, and discusses Skolem functions and Skolemization (this could have been more relaxed and helpful). We return to arithmetic in Chapter 12; there’s a compressed  discussion leading up to a version of Robinson’s model-theoretic proof of Tarski’s theorem of the arithmetic undefinability of arithmetic truth. But I rather doubt that this will be readily accessible to someone who hasn’t already read e.g. some of Kaye’s book on non-standard models of PA and met ideas like overspill.

The last three chapters are more advanced still, on saturation, automorphisms of recursively saturated structures, and (very briefly) stability. Are these topics for those just starting out on model theory? That’s a judgement call. But I suspect that the mode of presentation could be found quite challenging by many beginners — for me, more classroom asides in later chapters would have been welcome.

So as with Kossak’s earlier Mathematical Logic, then, I have rather different reactions to the two halves of Beginning Model Theory. But I’d say that the first eight or nine chapters do work very well under the advertised title (and I’ll be recommending them in the Study Guide). Later chapters are probably to be read in parallel with familiar moderately advanced texts like Marker’s classic.

Finally, bonus points for publishing very inexpensively with College Publications, and with tidy LaTeX layout too (however, they still can’t design a nice title page and verso!). But dock half a point for the number of minor typos …

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