Reading on Mathematical Logic 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. 

I fondly own the following books.
Logic


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*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


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*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.
