I previously published two logic books with CUP. But I recovered the copyright early in the pandemic, and as a small gesture to students in those very hard times I re-published them as open-access PDFs, entirely free to download. They are also now available as minimum cost paperbacks using the Amazon print-on-demand system (because this produces acceptable-quality books very inexpensively).
Before I retired from the University of Cambridge, it was my greatest good fortune to have secure, decently paid, university posts for forty years in leisurely times, with almost total freedom to follow my interests wherever they meandered. Like most of my contemporaries, for much of that time I didn’t really appreciate how extraordinarily lucky I was. To give a little back by way of heartfelt thanks, I have also put together three further student-oriented books, which are again free to download. Beginning Mathematical Logic is developed from the earlier much-used Teach Yourself Logic study guide.
So, in a bit more detail, here they all are!
Category Theory I: Notes towards a gentle introduction (2023) was a book version of the first half of a set of much-downloaded notes. It aimed to provide an accessible entry-point which doesn’t presuppose too much mathematical background. However, I have now (Jan 2024) withdrawn the pbk version, as a new edition will be published as Category Theory I: A gentle prologue in Feb 2024.
A pre-print of the new edition is available as a freely downloadable PDF. Comments and corrections will be most welcome! For more info, see here.
An Introduction to Formal Logic, based the first-year lecture course I gave for many years, was originally published by Cambridge University Press (2003, 2020). A corrected version of the second edition is now available as a freely downloadable PDF.
Many people, however, prefer if possible to work from a physical book. So you can get a print-on-demand copy of IFL as a very inexpensive large-format paperback from Amazon. There is also a nice but still inexpensive hardback version intended for libraries. For more info, see here, where you will find answers to exercises etc.
An Introduction to Gödel’s Theorems was first published in 2007 also by Cambridge University Press, with the second edition appearing in 2013. It was published in a philosophy series, but is full of theorems — so mathematics students should find it useful too.
A corrected version of the second edition is now available as a freely downloadable PDF. Again, for people who prefer to work from a physical book, there is a print-on-demand version as an inexpensive large format paperback. For more info, see here where you will find further support documents.
Gödel Without (Too Many) Tears is a much shorter book (2020, 2022) based on the lectures I used to give to undergraduate philosophers taking the Mathematical Logic paper. My notes have been tidied-up into a book format, now in its second edition. You can think of it as a cut-down version of the longer Gödel book, aiming to highlight some of the key technical facts about the incompleteness theorems in an accessible way.
If you want to self-study logic, or are looking for supplementary reading before or during a university course, how do you find your way around the very large literature old and new? Beginning Mathematical Logic (2022) provides a study guide, giving introductory overviews of the core topics and then recommending the best books for studying these topics enjoyably and effectively.