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I'm aware that things could get too broad if I'm not specific & careful enough, so please bear with me!

Having just "read" $\S 14.7$ of the titular book, I'm exhausted. It has $71$ exercises and I have done none of them. The previous sections of Chapter $14$ had numerous exercises, too, and, admittedly, I haven't done any of them either; the next, $31$ exercises. The text is becoming intractable without getting one's hands dirty (which is, I suppose, to be expected from a cursory reading).

I feel that there is a real gear change in this part of the book.

I am reading out of recreation and curiosity.

I think - and I hope - that I could do all the exercises on a second reading of the book, if & when I have time for them.

However, I could do with something at the moment to augment my understanding of the concepts involved in the chapter.

The subject of Chapter $14$ is "local truth".

What I'm looking for is multifaceted:

  • A synopsis of the chapter with an eye to building a foundation for the remaining chapters;

  • A selection of "key" exercises to focus on from $\S 14.7$ that are not too taxing, again, with an eye to the remainder of the book; and

  • Recommendations for further reading about the subject matter (like, say, Johnstone's, "Sketches of an Elephant [. . .]" or Mac Lane & Moerdijk's, "Sheaves in Geometry and Logic [. . .]").

Please help :)

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Shaun
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    Perhaps Section 3 of these notes of mine, written for an audience of philosophers of mathematics, are helpful? They contain a couple of concrete examples for local truth, and I'm open to any specific questions you might have! – Ingo Blechschmidt Jan 29 '20 at 19:33
  • Thank you, @IngoBlechschmidt! Those notes look very interesting :) – Shaun Jan 29 '20 at 20:53
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    I don't have a copy of the Elephant, but I've checked Mac Lane & Moerdijk and I don't think the $\Omega$-Set (or Heyting-valued set) point of view is used there at all, so there isn't any part of that book corresponding to Goldblatt's §14.7. – Robert Furber Feb 01 '20 at 04:44

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Especially if you're reading just for fun, there's a simple solution to finding a section intractable without doing lots of exercises: just don't do that section. Keep reading until you find something interesting, and if you find you need the earlier section to understand the latter, then go back. I think 14.7 will probably not turn out too important, though 14.6 is very important.

Mac Lane/Moerdijk is my recommendation for further reading. In fact, I would certainly have read it before Goldblatt. Sketches of an Elephant is more of an encyclopedic work for researchers.

Kevin Carlson
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  • Thank you for the advice. I'm finding Mac Lane & Moerdijk more difficult than Goldblatt so far though. I'm up to the first set of exercises. – Shaun Feb 04 '20 at 15:09