Praise not for our new Prime Minister, about whom the less said the better, but for her admirable logician father John Truss.
By chance, I had occasion recently to dip into his 1997 book Foundations of Mathematical Analysis (OUP) which I didn’t know before and which is excellent. It is my sort of book, in that there is a lot of focus on conceptual motivation and Big Ideas, and a relatively light hand with detailed proofs. E.g. if you want just a very few pages on Gödelian incompleteness, his treatment in the first chapter is exemplary. Or jumping to the end of the book, there is e.g. a really helpful broad-brush section on the ingredients of Gödel’s and Cohen’s independence proofs in set theory, and a very good chapter on constructive analysis and choice principles. In between, we get a story that takes us from the naturals to the integers to the reals to metric spaces and more (e.g. a nice chapter on measure and Baire category). OK, this is a tale which is often told, but I think John Truss’s version is particularly insightful and good at bringing out the conceptual shape of the developing story. So, recommended!
OUP have disappointingly let the book go out of print. A Djvu file can, however, be found at your favourite file depository.