GWT2 — up to the first incompleteness theorem

I have now revised Gödel Without (Too Many) Tears up to and including the pair of chapters on the first incompleteness theorem. You can download the current version up to Chapter 13 here.

For info: the chapter on quantifier complexity has been revised (adopting a more complex definition of Sigma_1 sentences, so that I don’t have to cheat later in saying that primitive recursive functions can be defined by Sigma_1 sentences). Then the chapter on primitive recursive functions has been slightly revised yet again. I have tried to make the chapter that proves that primitive recursive functions can indeed be defined by Sigma_1 sentences a bit more reader-friendly (the key ideas are elegantly simple: implementing them is unavoidably a bit messy). The chapter on the arithmetization of syntax is little altered. And finally in this instalment, the two chapters on the semantic and syntactic versions of the first incompleteness theorem are more or less untouched.

I’m still on track for getting a second edition out by around the end of October. It goes without saying that all comments and corrections will be gratefully received (and do please alert any students who might be interested in reading through and spotting typos or unclarities). Many thanks once again to David Furcy and Rowsety Moid for corrections and suggestions.

Added 24 Aug Corrected version uploaded.

2 thoughts on “GWT2 — up to the first incompleteness theorem”

  1. I’ve spotted a new Godel book that looks interesting: The Annotated Gödel: A Reader’s Guide to his Classic Paper on Logic and Incompleteness, by Hal Prince.

    It’s a new translation of the 1931 paper, with commentary. Like the translation done by Martin Hirzel in 2000 (Hirzel pdf), it modernises the notation and terminology (using ∀ rather than Π, saying “primitive recursive”, …), uses English rather than German for function and relations names, and translates with some flexibility (more than Hirzel). It also has much more commentary than Hirzel’s and looks like it translates the whole paper while Hirzel omits parts 3 and 4.

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