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I am looking for books to read, so as to dive into mathematical logical and related disciplines like set theory, model theory, and topos theory.

I have a decent background in category theory and algebra, analysis, topology, etc. but little in explicit logic or set theory aside from the first chapter of Munkres.

Any suggestions? I am interest in topics such as para-consistency, computability, and ill-founded logics.

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up vote 5 down vote accepted

The place to start, perhaps, is here:

This is a detailed annotated guide to a wide range of logic literature, at different levels of sophistication. You will be able to choose entry points to suit your background.

On non-paraconsistent logic, see in particular

which gives pointers to the literature. On computability, there is much to be said for Boolos, Burgess and Jeffrey,

I'm not sure what is meant by "ill-founded logics". For non-wellfounded set theory, see

which again gives more pointers. On topos theory, I still think it is worth starting with Robert Goldblatt's book:

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I fondly own the following books.


  • Peter Smith's An Introduction To Godel's Theorems is an excellent first introduction to logic and computability. Yes, that's the same Peter Smith whose answered your question.

Set theory

  • Goldrei's Classic Set Theory is a clear and well-motivated first introduction to the subject.

  • Jech's Set Theory is very highly regarded, and would be excellent for a second exposure to set theory (this is the book I really need to work through).

  • Also, you mentioned an interest in topos theory. I've never studied topos theory, but I think a good starting would be Lawvere's Sets for Mathematics which describes basic set theory from a categorial perspective. I think this will get you "in the mindset for topoi," so to speak.

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