An Introduction to Mathematical Logic (Dover Books on Mathematics)

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I'm a machine learning scientist and have been returning to this book since 2015 to read up on first order logic and Godel theorems. Unlike many books in this area, I think this book strikes a great balance between rigor and intuition. I love how the author first uses (un)decidability as a conceptual placeholder to explain concepts such as Godel expressibility before formalizing it later with recursion. This book has been my self-study guide to learning foundations, starting with formal languages and axioms as basic as counting notches on a paper, up till (almost) grasping proofs of Godel's incompleteness theorems.

Honestly, this book gets into the arcana of theories and systems a bit more than I needed, but it still served as a decent semi-introduction/review for a high school math teacher / computer programmer who was trying to help out a former student taking an introductory class in mathematical logic. If you are in a similar situation as I was, I recommend reading the start of each chapter in detail and when it gets too theoretical just skim.Also, for some reason the first chapter dives pretty hard into advanced concepts like formal systems, relations, decidability, etc. that are arguably more difficult than the bulk of the following chapters. The author recommends to "cover it as needed" in the preface. This is good advice as the next few chapters are a bit easier and more on topic.Anyway, aside from being rather challenging in parts for a non-expert, it is also extremely well organized and readable with an index etc., hence a reasonable choice even for a less advanced mathematician like myself. If you are looking to touch on more advanced topics (the work of Godel, Tarski, Church, etc.), it will do that too.

Book is well written, except on one parts: now and then the proofs for theorems, lemmas etc. are quite unfinished and as such demand working on them. The book itself is broad and detailed othervicely with an excellent set of exercises and reviews of the theories from basic theories to computability and somewhat decision theory. Indeed, this one can be warmly recommed from beginners to advanged students and hobbyist alike who demand more exercises and good source book to bookstand.

At first, I didn't really like this book, but it was okay...but I kept studying in...off and on. Meanwhile, I studied many other logic books as well. However, over time, I realized how priceless this book really was. It's quite excellent, especially when you get further in. It also covers lots of material skipped by other books.

This is by far one of the best mathematics books I have read to date. The author clearly has a solid understanding of the material and didn't just copy and paste from previous works in the field.Highly Recommend if you're interested in mathematics, computer science or philosophy.

One of the best books ever written on Logica Matemática!A must-read!

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