New Textbook on Incompleteness

Uncategorized by rzach

I’m teaching the incompleteness theorems (and related material) this term, and of course I’m using the Open Logic Project as a text. The relevant sections are based on Jeremy Avigad’s notes, which originally were meant as a supplement to Epstein & Carnielli’s textbook Computability. I’ve spent a fair bit of time revising them, and making them independent of that text. That meant adding a bunch of material, reformatting things, adding explanations and examples, etc. I think it’s now in sufficiently good shape that I can share it. However, it’s by no means done (we’re only halfway through the semester). I’m waiting to hear what else my students want to hear about; and I’ll update the project with additional chapters from the OLP (perhaps yet to be written). The most unusual aspect of it so far is perhaps that I’m doing everything in natural deduction, including arithmetization of provability.

The most recent PDF version should be available here, but I’ll also attach the current version to this post. All the actual material (with the exception of the chapter summaries and the front matter) comes from the Open Logic Text. The code to produce the text in this version is on GitHub. As usual, suggestions more than welcome!

Incompleteness and Computability

4 comments

  2. Erich Reck

    Hi Richard,

    I just glanced briefly at your “Incompleteness and Computability”, since I will probably teach that class next year again myself (I do so every few years). I was led to page 4, where you write:

    “But Georg Cantor showed that it was impossible to take the infinite at face value.”

    Shouldn’t it say “… that it was impossible NOT to take the infinite at face value”? Or instead: “… that it was POSSIBLE to take the infinite at face value”?

    Best,
    Erich

  3. Richard Zach

    Jeremy says, yes, “possible”. Fixed in repository.

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