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# MAA Reviews

## Foundations and Mathematical Logic: Surveys

Beth, Evert. The Foundations of Mathematics Amsterdam: North-Holland, 1959.

* Eves, Howard W. Foundations and Fundamental Concepts of Mathematics, Boston, MA: PWS-Kent, 1990. Third Edition.

** Mac Lane, Saunders. Mathematics, Form and Function New York, NY: Springer-Verlag, 1986.

* Mostowski, Andrzej. Thirty Years of Foundational Studies New York, NY: Barnes and Noble, 1966.

* Wilder, Raymond L. Introduction to the Foundations of Mathematics, Melbourne, FL: Robert E. Krieger, 1980. Second Edition.

## Foundations and Mathematical Logic: Logic

* Barwise, Jon and Etchemendy, John. The Liar: An Essay on Truth and Circularity New York, NY: Oxford University Press, 1987.

* Boole, George. An Investigation of the Laws of Thought Mineola, NY: Dover, 1951.

Copi, Irving Marmer. Symbolic Logic, New York, NY: Macmillan, 1973. Fourth Edition.

Jeffrey, Richard C. The Logic of Decision, Chicago, IL: University of Chicago Press, 1983. Second Edition.

Quine, Willard Van Orman. Methods of Logic, New York, NY: Holt, Rinehart and Winston, 1972. Third Edition.

Suppes, Patrick C. Introduction to Logic New York, NY: Van Nostrand Reinhold, 1957.

Venn, John. Symbolic Logic, New York, NY: Chelsea, 1971. Second Edition.

Venn, John. The Principles of Inductive Logic, New York, NY: Chelsea, 1973. Second Edition.

## Foundations and Mathematical Logic: Mathematical Logic

Andrews, Peter B. An Introduction to Mathematical Logic and Type Theory: To Truth Through Proof New York, NY: Academic Press, 1986.

* Barwise, Jon and Etchemendy, John. The Language of First-Order Logic Stanford, CA: Center for Study of Language Information, 1990.

*** Barwise, Jon, ed. Handbook of Mathematical Logic Amsterdam: North-Holland, 1977.

Bell, J.L. and Machover, Moshe. A Course in Mathematical Logic Amsterdam: North-Holland, 1977.

Boolos, George S. The Unprovability of Consistency: An Essay in Modal Logic New York, NY: Cambridge University Press, 1979.

* Boolos, George S. and Jeffrey, Richard C. Computability and Logic, New York, NY: Cambridge University Press, 1974, 1989. Third Edition.

** Crossley, J.N., et al. What is Mathematical Logic? New York, NY: Oxford University Press, 1972.

Curry, Haskell B. Foundations of Mathematical Logic Mineola, NY: Dover, 1977.

** Davis, Martin D., ed. The Undecidable: Basic Papers on Undecidable Propositions, Unsolvable Problems and Computable Functions New York, NY: Raven Press, 1965.

* Ebbinghaus, H.-D.; Flum, J.; and Thomas, W. Mathematical Logic New York, NY: Springer-Verlag, 1984.

* Enderton, Herbert B. A Mathematical Introduction to Logic New York, NY: Academic Press, 1972.

Goodstein, R.L. Development of Mathematical Logic New York, NY: Springer-Verlag, 1971.

Hatcher, William S. The Logical Foundations of Mathematics Elmsford, NY: Pergamon Press, 1982.

Hilbert, David. and Ackermann, W. Principles of Mathematical Logic New York, NY: Chelsea, 1950.

* Kleene, Stephen C. Mathematical Logic New York, NY: John Wiley, 1967.

*** Kleene, Stephen C. Introduction to Metamathematics Amsterdam: North-Holland, 1974.

Kneebone, G.T. Mathematical Logic and the Foundations of Mathematics New York, NY: Van Nostrand Reinhold, 1963.

* Mendelson, Elliott. Introduction to Mathematical Logic, Belmont, CA: Wadsworth, 1987. Third Edition.

* Monk, J. Donald. Mathematical Logic New York, NY: Springer-Verlag, 1976.

** Nagel, Ernest and Newman, James R. Godel's Proof New York, NY: New York University Press, 1958.

Rosser, J. Barkley. Logic for Mathematicians, New York, NY: Chelsea, 1978. Second Edition.

* Tarski, Alfred. Logic, Semantics, Metamathematics, Indianapolis, IN: Hackett, 1983. Second Edition.

## Foundations and Mathematical Logic: Philosophy of Mathematics

Aspray, William and Kitcher, Philip, eds. History and Philosophy of Modern Mathematics Minneapolis, MN: University of Minnesota Press, 1988.

* Benacerraf, Paul and Putnam, Hilary. Philosophy of Mathematics: Selected Readings, Englewood Cliffs, NJ: Prentice Hall, 1964, 1989. Second Edition.

Cohen, Jonathan. An Introduction to the Philosophy of Induction and Probability New York, NY: Oxford University Press, 1989.

Hintikka, Jaakko. The Philosophy of Mathematics New York, NY: Oxford University Press, 1969.

* Kitcher, Philip. The Nature of Mathematical Knowledge New York, NY: Oxford University Press, 1984.

Korner, Stephan. The Philosophy of Mathematics: An Introductory Essay, Mineola, NY: Dover, 1968, 1986. Second Edition.

*** Lakatos, Imre. Proofs and Refutations: The Logic of Mathematical Discovery New York, NY: Cambridge University Press, 1976.

Quine, Willard Van Orman. Pursuit of Truth Cambridge, MA: Harvard University Press, 1990.

* Quine, Willard Van Orman. Philosophy of Logic, Cambridge, MA: Harvard University Press, 1986. Second Edition.

Quine, Willard Van Orman. The Ways of Paradox and Other Essays, Cambridge, MA: Harvard University Press, 1976. Revised and Enlarged Edition.

** Russell, Bertrand. Introduction to Mathematical Philosophy New York, NY: Macmillan, 1920.

Wang, Hao. Beyond Analytic Philosophy: Doing Justice to What We Know Cambridge, MA: MIT Press, 1986.

* Wittgenstein, Ludwig. Remarks on the Foundations of Mathematics, Cambridge, MA: MIT Press, 1978. Revised Edition.

## Foundations and Mathematical Logic: Set Theory

Baumgartner, James E.; Martin, Donald A.; and Shelah, Saharon, eds. Axiomatic Set Theory Providence, RI: American Mathematical Society, 1984.

Bell, J.L. Boolean-Valued Models and Independence Proofs in Set Theory New York, NY: Clarendon Press, 1977.

Bernays, Paul. Axiomatic Set Theory, Mineola, NY: Dover, 1991.

Bourbaki, Nicolas. Elements of Mathematics: Theory of Sets Reading, MA: Addison-Wesley, 1968.

Dales, H.G. and Woodin, W.H. An Introduction to Independence for Analysts New York, NY: Cambridge University Press, 1987.

Devlin, Keith J. The Axiom of Constructibility: A Guide for the Mathematician New York, NY: Springer-Verlag, 1977.

* Devlin, Keith J. Fundamentals of Contemporary Set Theory New York, NY: Springer-Verlag, 1979.

* Enderton, Herbert B. Elements of Set Theory New York, NY: Academic Press, 1977.

* Fraenkel, Abraham A. Abstract Set Theory, Amsterdam: North Holland, 1953, 1966. Third Edition.

** Fraenkel, Abraham A.; Bar-Hillel, Yehoshra; and Levy, Azriel. Foundations of Set Theory, Atlantic Highlands, NJ: Humanities Press, 1973. Second Revised Edition.

* Godel, Kurt. The Consistency of the Axiom of Choice and of the Generalized Continuum-Hypothesis with the Axioms of Set Theory Princeton, NJ: Princeton University Press, 1961.

*** Halmos, Paul R. Naive Set Theory New York, NY: Springer-Verlag, 1974.

Hrbacek, Karel and Jech, Thomas. Introduction to Set Theory, New York, NY: Marcel Dekker, 1978, 1984. Second Revised Edition.

* Jech, Thomas. The Axiom of Choice Amsterdam: North-Holland, 1973.

Kamke, E. Theory of Sets Mineola, NY: Dover, 1950.

** Kunen, Kenneth. Set Theory: An Introduction to Independence Proofs, New York, NY: Elsevier Science, 1983.

* Kuratowski, K. and Mostowski, Andrzej. Set Theory with an Introduction to Descriptive Set Theory Amsterdam: North-Holland, 1976.

Levy, Azriel. Basic Set Theory New York, NY: Springer-Verlag, 1979.

* Moschovakis, Yiannis N. Descriptive Set Theory Amsterdam: North-Holland, 1980.

Quine, Willard Van Orman. Set Theory and Its Logic, Cambridge, MA: Harvard University Press, 1969. Revised Edition.

* Roitman, Judith. Introduction to Modern Set Theory New York, NY: John Wiley, 1990.

** Vilenkin, N. Ya. Stories About Sets New York, NY: Academic Press, 1968.

## Foundations and Mathematical Logic: Computability

Cutland, Nigel. Computability: An Introduction to Recursive Function Theory New York, NY: Cambridge University Press, 1980.

*** Davis, Martin D. Computability and Unsolvability Mineola, NY: Dover, 1982.

Odifreddi, P.C. Classical Recursion Theory Amsterdam: North-Holland, 1989.

* Pour-El, Marian B. and Richards, J. Ian. Computability in Analysis and Physics New York, NY: Springer-Verlag, 1989.

*** Rogers, Hartley, Jr. Theory of Recursive Functions and Effective Computability Cambridge, MA: MIT Press, 1987.

Soare, Robert I. Recursively Enumerable Sets and Degrees: A Study of Computable Functions and Computably Generated Sets New York, NY: Springer-Verlag, 1987.

* Uspenskii, V.A. Post's Machine Moscow: MIR, 1983.

## Foundations and Mathematical Logic: Model Theory

Baldwin, John T. Fundamentals of Stability Theory New York, NY: Springer-Verlag, 1988.

* Bridge, Jane. Beginning Model Theory: The Completeness Theorem and Some Consequences New York, NY: Clarendon Press, 1977.

*** Chang, C.C. and Keisler, H. Jerome. Model Theory, Amsterdam: North-Holland, 1973, 1990. Third Edition.

* Hodges, W. Building Models by Games New York, NY: Cambridge University Press, 1985.

Kopperman, Ralph. Model Theory and Its Applications Boston, MA: Allyn and Bacon, 1972.

* Lightstone, A.H. Mathematical Logic: An Introduction to Model Theory New York, NY: Plenum Press, 1978.

Lightstone, A.H. and Robinson, Abraham. Nonarchimedean Fields and Asymptotic Expansions Amsterdam: North-Holland, 1975.

* Morley, M.D., ed. Studies in Model Theory Washington, DC: Mathematical Association of America, 1973.

** Robinson, Abraham. Introduction to Model Theory and to the Metamathematics of Algebra Amsterdam: North-Holland, 1974.

Robinson, Abraham. Complete Theories, Amsterdam: North-Holland, 1977. Second Edition.

## Foundations and Mathematical Logic: Nonclassical Logic

Beeson, Michael J. Foundations of Constructive Mathematics: Metamathematical Studies New York, NY: Springer-Verlag, 1985.

** Bishop, Errett. Foundations of Constructive Analysis New York, NY: McGraw-Hill, 1967.

* Bridges, Douglas S. and Richman, Fred. Varieties of Constructive Mathematics New York, NY: Cambridge University Press, 1987.

Dummett, Michael. Elements of Intuitionism New York, NY: Clarendon Press, 1977.

** Heyting, A. Intuitionism: An Introduction, Amsterdam: North-Holland, 1976. Third Revised Edition.

** Troelstra, A.S. and van Dalen, Dirk. Constructivism in Mathematics: An Introduction Amsterdam: North-Holland, 1988.

van Dalen, Dirk, ed. Brouwer's Cambridge Lectures on Intuitionism New York, NY: Cambridge University Press, 1981.

## Foundations and Mathematical Logic: Special Topics

Frege, Gottlob. On the Foundations of Geometry and Formal Theories of Arithmetic New Haven, CT: Yale University Press, 1971.

Goldblatt, Robert. Topoi: The Categorical Analysis of Logic Amsterdam: North-Holland, 1979.

* Gonshor, Harry. An Introduction to the Theory of Surreal Numbers New York, NY: Cambridge University Press, 1986.

Henkin, Leon; Monk, J. Donald; and Tarski, Alfred. Cylindric Algebras, Amsterdam: North-Holland, 1971. 2 Vols.

Hindley, J. Roger and Seldin, Jonathan P. Introduction to Combinators and $ambda$-Calculus New York, NY: Cambridge University Press, 1986.

* Takeuti, Gaisi. Proof Theory Amsterdam: North-Holland, 1975.

* Tarski, Alfred. Ordinal Algebras Amsterdam: North-Holland, 1956.