Set Theory: A First Course (Cambridge Mathematical Textbooks)

I’m only in the first chapter but have skimmed the entire book. This is the kind of book that is ideal for self study: (1) it covers a sufficiently narrow topic so as not to get bogged down, (2) the material requires thought but no special intellectual athletic prowess like differential geometry or Hilbert spaces do, (3) it’s very well laid out with an index just for special symbols and operators, worth the price of the book in itself, and (4) it’s a slim volume, easy to carry around and hold, like the “Student’s Guide to …” series (most by Daniel Fleisch) (which I also highly recommend for the same reasons).This book is manufactured as print on demand, so the “hardcover” version is basically two boards glued to a glued-bound POD cheap paperback book. I always find cheap binding using generic printer paper to manufacture a reference book to be sad. But I guess I’d rather be sadly reading good content in a real book than reading a technical/reference book on the screen of a kindle app (where would I attach my post-its?).

Using the text as a reference in refreshing my skills in Set Theory. Accomplishing my goal!

Cunningham writes carefully and clearly. The book begins with a short introduction to logic notation and its meaning. The ZF axioms are listed together on page 24 of chapter one before used to develop the theory axiomatically, beginning in chapter two.A likely comparison to this book is Herbert Enderton's Elements of Set Theory (1977). Cunningham's book is a cleaner presentation. One difference is that Cunningham does not give a construction of the real numbers, as Enderton does.In his References, Cunningham lists 14 books. Set theory textbooks listed are Enderton's Elements, Halmos' Naive ST, Kunen's The Foundations of Mathematics, Levy's Basic ST, and Moschovakis' Notes on ST. Also listed, among others, are Potter's ST and Its Philosophy, and Enderton's A Mathematical Introduction to Logic.To my mind, Cunningham's Set Theory : A First Course is the best introduction to set theory in the English language.

The content is good but the author introduces symbols without defining them explicitly, expecting you to understand from context. The symbol notation is also sometimes inconsistent. The equations also appear very small on the ipad but PC is fine.

I graduated in mathematics many, many years ago but I always worked on other things, never in Math. I read this book and did almost all the exercises in about 6 months of self-study. The book is simply excellent, very well written, I recommend it 100%. I even wrote to the author several times and he always responded promptly with kindness. The best book at its level on the market.