There are currently four Big Red Logic Books. The first two were previously published by CUP. But I recovered the copyright early in the pandemic, and as a small gesture to students in these very hard times they are now published as open-access PDFs, entirely free to download. They are also 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 two further student-oriented books, which are again free to download. In particular, Beginning Mathematical Logic is developed from the earlier much-used Teach Yourself Logic study guide.
So, in a bit more detail, here they are!
An Introduction to Formal Logic was originally published by Cambridge University Press (2003, 2020). It began life as lecture notes for a course for first-year philosophers which I taught for many years.
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 also 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 many 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 a very inexpensive large format book from Amazon.
For more info, see here where you will also find further support documents.
NEW EDITION! Gödel Without (Too Many) Tears is a much shorter book (2020) 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.
This book is again available as a PDF. There is also an extremely inexpensive print-on-demand book available from Amazon, and a hardback too.
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.
This book too is available as a PDF. Again, there is also a very inexpensive print-on-demand book available from Amazon