[Math] Books on logic, proof theory and set theory

logicphilosophyproof-theoryreference-requestset-theory

I graduated in Computer Science at University of Bologna in Italy some years ago.
For various reasons now I am discovering a back interest in mathematic logic higher than I was a student.

I have only a pair of university books about the subject. Now I am reading that books and I am enhancing the not so developed concepts using mainly Wikipedia.
Because of this reason, maybe what I am going to write consecutively is a bit confused.

Now I am looking for the minimal list of books that cover the following areas:

  • All kinds of logic: classical, intuitionstic, relevance, etc…
  • Proof theory
  • Set theory
  • Philosophical implications

For each of these areas I am interested its history too.

Every help is really appreciated.

Best Answer

There's a long and detailed annotated reading list of books on all kinds of areas of logic, at various levels, downloadable from

http://logicmatters.net/students/tyl/

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