Linked bibliography for the SEP article "Second-order and Higher-order Logic" by Herbert B. Enderton

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  • Boolos, George, 1975.   “On Second-Order Logic,” The Journal of Philosophy, 72: 509–527.   Also in Logic, Logic, and Logic, by George Boolos, Cambridge, MA: Harvard University Press, 1998, pp. 37–53. (Scholar)
  • Church, Alonzo, 1956.   Introduction to Mathematical Logic, Volume 1.   Princeton: Princeton University Press. (Scholar)
  • –––, 1972.   “Axioms for Functional Calculi of Higher Order,” in Logic and Art: Essays in Honor of Nelson Goodman, Richard S. Rudner and Israel Scheffler (eds.), Indianapolis and New York: Bobbs-Merrill Company, pp. 197–213. (Scholar)
  • Enderton, Herbert B., 2001.   A Mathematical Introduction to Logic, second edition.   San Diego: Academic Press. (Scholar)
  • Fagin, Ronald, 1974.   “Generalized First-Order Spectra and Polynomial-Time Recognizable Sets,” in Complexity of Computation, Richard M. Karp (ed.), SIAM-AMS Proceedings, vol. 7, Providence: American Mathematical Society, pp. 43–73. (Scholar)
  • Garland Stephen J., 1974.   “Second-Order Cardinal Characterizability,” in Axiomatic Set Theory, Thomas J. Jech (ed.), Proceedings of Symposia in Pure Mathematics, vol. 13, part 2, Providence: American Mathematical Society, pp. 127–146. (Scholar)
  • Grzegorczyk, Andrzej, A. Mostowski, and C. Ryll-Nardzewski, 1958.   “The Classical and the ω-Complete Arithmetic,” The Journal of Symbolic Logic, 23: 188–205. (Scholar)
  • Henkin, Leon, 1950.   “Completeness in the Theory of Types,” The Journal of Symbolic Logic, 15: 81–91. (Scholar)
  • Hintikka, K. Jaakko, 1955.   “Reductions in the Theory of Types,” in Two Papers on Symbolic Logic, Acta Philosophica Fennica, No. 8, Helsinki, pp. 57–115. (Scholar)
  • Montague, Richard, 1965.   “Reductions of Higher-Order Logic,” in The Theory of Models, J. W. Addison, Leon Henkin, and Alfred Tarski (eds.), Amsterdam: North-Holland Publishing Co., pp. 251–264. (Scholar)
  • Mostowski, Andrzej, 1961.   “Formal System of Analysis Based on an Infinitistic Rule of Proof,” in Infinitistic Methods, Warsaw: Państwowe Wydawnictwo Naukowe, and Oxford, London, New York, and Paris: Pergamon Press, pp. 141–166. (Scholar)
  • Orey, Steven, 1956.   “On ω-Consistency and Related Properties,” The Journal of Symbolic Logic, 21: 246–252. (Scholar)
  • Shapiro, Stewart, 1991.   Foundations without Foundationalism: A Case for Second-Order Logic.   Oxford: Oxford University Press. (Scholar)
  • Simpson, Stephen, 1999.   Subsystems of Second Order Arithmetic.   Berlin: Springer. (Scholar)
  • Väänänen, Jouko, 2001.   “Second-Order Logic and Foundations of Mathematics,” The Bulletin of Symbolic Logic, 7: 504–520. (Scholar)

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