Here is the draft final chapter of Part I of *Beginning Mathematical Logic* — so this is the last of the group of chapters on core topics at an elementary level. This one on proof theory is newly written; comments will therefore be particularly welcome.

Having got this far, I am well aware that there are now some mismatches in the level/breadth of the overviews in the various chapters, and also places which call for more cross-references. For example, I need to go back to the overview on set theory to say just a paragraph or so more about ordinals, in order to make a better connection with the use of small ordinals in the current chapter when waving my arms at Gentzen’s consistency proof. So smoothing out the coverage of Part I of the Study Guide is a next task. But at least there is now a full draft to play with.

Peter FI meant to mention this at one point but I don’t think I ever did. Tin Lok Wong, who did his PhD under Richard Kaye in models of arithmetic, has two sets of lecture notes on his website that I think are worth looking at. One is on the consistency of arithmetic blog.nus.edu.sg/matwong/teach/cons/ and one is on models of arithmetic blog.nus.edu.sg/matwong/teach/modelarith/. I would say they are presented at the graduate level, a lot of the material is very terse, but still there is a lot of good exposition and connection of ideas in the sections I’ve read of both. They might be worth looking into as recommendations for the advanced sections on model theory and proof theory.

Peter SmithMany thanks for this! These notes, at a fairly quick glance, do indeed look pretty impressive, and might indeed be worth recommending for Part III.