 | Logic, Sets, and Recursion (Jones and Bartlett Books in Mathematics) by Robert L. Causey
Buy used from: $3.64 My intro logic book, still the best around
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 | First-Order Logic by Raymond M. Smullyan
Buy new: $9.95 / Used from: $5.00 Concise yet in-depth. Smullyan uses trees to explain first-order metatheory.
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 | Introduction to Mathematical Logic (University Series in Undergraduate Mathematics) by Elliott Mendelson
Buy used from: $9.98 Densely technical, but covers a lot of ground, especially recursion theory. Includes a bit on free logic and second-order logic.
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 | Axiomatic Set Theory by Patrick Suppes
Buy new: $10.10 / Used from: $5.95 Clear, concise account of Zermelo-Fraenkel set theory with the Axiom of Choice. Talks about historical background, too.
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 | Theory of Sets by E. Kamke
Buy used from: $2.29 Good non-axiomatic account of set theory. A nice companion to Suppes' more formal approach.
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 | Metalogic: An Introduction to the Metatheory of Standard First Order Logic by Geoffrey Hunter
Buy new: $24.04 / Used from: $7.78 Clear, readable, well-written intro to first-order metatheory, rigorous without being soporific. The writing style is almost conversational, not the usual I'm-fearfully-smart-so-bow-your-head tone.
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 | A New Introduction to Modal Logic by M.J. Cresswell
Buy new: $119.32 / Used from: $70.00 Probably the best available intro to modal logics. Covers a lot of ground, though the style is rather dull.
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 | An Introduction to Non-Classical Logic by Graham Priest
Buy used from: $15.00 Mainly about conditionals, but contains much useful info on deviant logics. Priest is a crazy philosopher, but a wonderful expositor and a very sophisticated logician.
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 | Logic: A Very Short Introduction (Very Short Introductions) by Graham Priest
Buy new: $8.54 / Used from: $4.27 No real technical details, and of little use for the student, but a pleasure to read. Contains several amusing puzzles. Certainly worth the price.
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 | Introduction to Mathematical Philosophy by Bertrand Russell
Buy new: $7.88 / Used from: $3.44 A classic, written in prison. Very clear and readable, as Russell always is, and requires no technical prerequisites. Ideal intro to Russell's phil. math.
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 | Principia Mathematica to *56 (Cambridge Mathematical Library) by Alfred North Whitehead
Buy new: $72.00 / Used from: $18.75 I don't recommend actually *reading* PM, but it is useful as a reference. Also can be Xeroxed to make a nice wallpaper.
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 | The Foundations of Arithmetic: A Logico-Mathematical Enquiry into the Concept of Number by Gottlob Frege
Buy new: $19.80 / Used from: $9.12 This is the first mathematically competent discussion of phil. math. One of the Great Books, though not often read by Great Bookists. A must-read for analytic philosophers.
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 | A Shorter Model Theory by Wilfrid Hodges
Buy new: $45.53 / Used from: $39.95 The best of its kind, except for the bigger book, which I can't afford.
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| Foundations of Analysis by Edmund Landau
Buy used from: $18.00 Not a textbook--a GOOD book! Starts with Peano's axioms and builds the real numbers in the bare minimum of theorems. Mathematical exposition that reads like poetry.
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 | Understanding the Infinite by Shaughan Lavine
Buy new: $25.08 / Used from: $10.99 Wonderful book on a fascinating subject. Want to know the REAL Cantor? Start here! Also much info on development of math, esp. analysis & set theory.
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 | Elementary Logic: Revised Edition by W. V. Quine
Buy new: $18.45 / Used from: $9.45 Learn at the feet of the Logician, boys and girls. Imagine having Quine for your intro logic teacher at Harvard! Lucky bastards!
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 | Methods of Logic: Fourth Edition by W. V. Quine
Buy new: $23.94 / Used from: $3.50 A good follow-up to "Elementary Logic". I would list all of Quine's logic books here, but you can find them for yourself.
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