Good books on mathematical logic?
Solution 1:
For my work in this area, I refer to :
- Richard Epstein "Classical Mathematical Logic"
- Wolfgang Rautenberg "A Concise Introduction to Mathematical Logic"
- Jon Barwise "Handbook of Mathematical Logic"
- Jean Heijenoort "From Frege to Gödel"
- We Li "Mathematical Logic"
Rautenberg has a lot of examples, exercise, but is very heavy going (at least for me). Epstein is fairly recent and very well laid out. Barwise is the most comprehensive for when you need to deep dive.
Solution 2:
A book that should be read by everyone in mathematics regardless of level is Wolfe's A Tour Through Mathematical Logic.
It's simply a compulsory read, I couldn't put it down. It gives a broad overview of mathematical logic and set theory along with its history, and it is absolutely beautifully written. That's the best place for anyone to begin.
Solution 3:
Ebbinghaus, Flum and Thomas. Mathematical Logic (Amazon)
Solution 4:
Shoenfield's "Mathematical Logic". The notation is a bit dated, but the exercises are great.