It is very good to note that the excellent A Friendly Introduction to Mathematical Logic by Christopher Leary and Lars Kristainsen is now available as PDF for free download from the book’s webpage here (as well as still being available as a very reasonable paperback).
Looking ahead a few weeks, I am not planning to do a serious in-depth revision of the Teach Yourself Logic Study Guide for 2018, as I really, really, must concentrate on the second edition of my intro book. But I may well do a very modest ‘maintenance upgrade’, in particular updating links where other books have become freely (but legally!) available.
Occasionally people try to post comments here noting that this or that book is electronically available at the-file-repository-of-which-we-shall-not-speak, comments which I have to delete. But I am always pleased to hear about cases like this where authors listed in the Guide have themselves made their work free-to-download: so are there any more cases I should know about?
Proof theory in this book means that any tautology can be written down. How can you recommend such rubbish to anyone?
This book gives an axiomatic presentation of FOL, and it’s not uncommon to set things up so that either every tautological formula is an axiom, or so that you can draw tautological conquences in one step. Sure, that’s no use to someone who wants to draw out the fine structure of propositional inferences, so to speak. But every logic book is about what it is about and not some other thing, and this text is concentrating completeness and incompleteness. (After all, even Kreisel — for all his deep interest in proof theory — in his Elements of Mathematical Logic just cheerfully defines propositional theorems to be tautologies … fair enough, surely, given his concerns.)