I’m a civil engineer that spends all of its free time (with the permission of my wife and my two children) studying set theory and mathematical logic. For instance, I’ve read and enjoyed “Axiomatic set Theory” by Suppes, Enderton’s “Elements of set theory”,”Mathematical logic” by Shoenfield or “A course in mathematical logic” by Bell and Machover. Now, my goals are the history and the development of these two mathematical branches.
In this sense I’m reading “Foundations of Set Theory” by Fraenkel, Bar-hilleil and levy or “Labyrinth of thought” by José Ferreirós and I would like to have in the same line as the above good books in the foundations of mathematical logic.
Thank you in advance
The reading list/study guide linked at http://www.logicmatters.net/students/tyl/ is only half done yet [reminder to self to get on with it!] but might contain one or two helpful suggestions.
You might like the book “Foundations of Mathematics” by William S. Hatcher.
You might be interested in van Heijenoort’s From Frege To Gödel: A Source Book in Mathematical Logic, 1879-1931.
On a different line, I recommend Dauben’s biography of Cantor, and his more recent Battle for Cantorian Set Theory.
Introduction to Mathematical Thinking is a very good book in my opinion. It is even more effective when you read it along with the courseware of the course by the same name.
Foundations of Mathematical Logic by Haskell B. Curry is a good book on this topic.
If you are interest in knowing it’s application in Computer Science then you can go for Discrete Mathematical Structures With Applications to Computer Science – Jean Paul Tremblay, Rampurkar Manohar .