What are some good books on logic and set theory?

[ Editor: an unsigned reading list, as collected. ]

LOGIC

What Is The Name Of This Book? -Smullyan
    Explores concepts of modern logic, including Goedel's theorem,
    through entertaining puzzles.

Goedel, Escher, Bach  -Hofstadter
    A popular examination of the concepts of self-reference in logic,
    art, and music.

Metalogic  -Geoffrey Hunter
    A good elementary introduction to the modern theory of logic.

Naive Set Theory, by P. R. Halmos:
    To understand the basic reasoning methods underlying nearly all of
    mathematics; this book is intended as a simple introduction for
    beginning mathematicians.  It is remarkably clear, elementary in
    presentation, and short (~100-150 pages).  It contains
    ``everything a practicing mathematician needs to know about set
    theory; learn it, then forget it.''  Much fundamental knowledge:
    sets, functions, equivalence relations and classes, order
    relations, axiom of choice, Zorn's lemma, well-ordering principle,
    cardinal numbers, ordinal numbers.  Probably the single most useful
    book for understanding everything else.  I would read it even if I
    weren't a mathematician, in order to get some insight into
    mathematical thinking.

Introduction to Mathematical Logic (3rd Edition)
Elliott Mendelson
Wadsworth and Brooks, Monterey CA, 1987
    -- Besides propositional and predicate logic, he covers formal
    -- number theory, axiomatic set theory, and computability.

An Introduction to Mathematical Logic: To Truth Through Proof
Peter B. Andrews
Academic Press, Orlando FL, 1986
    -- Additional topics here include type theory (i.e. typed
    -- lambda calculus) as a useful second-order logic.

Logic and Structure
D. van Dalen
Springer-Verlag,  Berlin, 1983
    -- A natural deduction approach

Logic for Computer Science: Foundations of Automatic Theorem Proving
Jean H. Gallier
Harper and Row, New York, 1986
    -- Uses Gentzen deduction. Also provides a formal basis for
    -- resolution. Lots of material. Proofs are quite detailed.

Foundations of Logic Programming (2nd Edition)
J.W. Lloyd
Springer-Verlag, Berlin, 1987
    -- Covers the fundamentals of resolution theorem proving.

In article <3936@pasteur.Berkeley.Edu> dchinn@cory.Berkeley.EDU (Donald
Chinn) writes:
>Anybody have a good suggestion on book(s) on logic.
>I already have Enderton's book, and I would like to read
>another one (just to get a different treatment).

I can heartily recommend "An Introduction to Modal Logic" by
G.E. Hughes and M.J. Creswell.  This gives an excellent treatment of
many different modal logics.

-- Pat Place  {rutgers,princeton}!petsd!pedsgd!pat