Books on Mathematical Logic

  • #1

Main Question or Discussion Point

Sorry to have two threads up at the top of the Science Book Discussion forum, but I couldn't find a thread for this. I'm interested in learning some mathematical logic. Here are the books I'm considering, please tell me what you think of them or suggest better alternatives.

Mathematical Logic - Kleene. What I plan to get. I would consider getting Tarski's book as well. Seems to be a good introduction to logic, and complete (Logic pun, get it?) and a very reasonable price.

Introduction to Metamathematics - Beeson. I don't know much about it, but it seems like it's good. Any suggestions for a god meta-math book?

First order logic - Smullyan. Supposed to be good but hard.

Axiomatic Set Theory - Suppes. I understand naive set theory pretty well, and this looks like a good course in Axiomatic Set theory.

Set Theory and Its Philosophy - Looks pricey, but supposed to be good. Might consider it.

Axiomatic Set Theory - Bernays. Supposed to be a well thought out look at set theory.

Principia Mathematica - Russell and Whitehead. Maybe someday! Well, at least publishers have stopped sniffing glue and are selling the three volumes for $50 rather than the previous price of $700(!) for the set. Or maybe the copyright expired. (Seriously, $700!)

So there you have it! Please tell me if my books are good, or recommend alternatives. I would also like some recommendations on other types of logic, like modal logic and whatever. Some books on model theory would be nice. What else is there to logic?
 

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  • #2
xristy
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  • #3
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Two books on categorical logic, a sort of meta-logical theory derived from category theory, that are very insightful are Toposes, Triples, and Theories and Topoi: The Categorial Analysis of Logic. I prefer the Categorical Approach to logic as it takes less statements as axioms than logic or other mathematical theories.
 

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