Homepage of Yong Cheng

Teaching

Undergraduate Courses taught
Graduate Courses taught

Teaching Award
  • Wuhan University 2016-2017 Academic Year Undergraduate Outstanding Teaching Performance Award

Some English reference books for some fields

Fundamentals of Mathematical Logic

  • Herbert B. Enderton. A mathematical introduction to logic (2nd ed.), Boston, MA: Academic Press, 2001.

  • John L.Bell, M. Machover.  A Course in Mathematical Logic, Elsevier, 2015.

  • George Boolos,  John Burgess and Richard Jeffrey. Computability and Logic (5th ed.), Cambridge: Cambridge University Press, 2002.

  • H.D.Ebbinghaus, J.Flum, W.Thomas. Mathematical Logic (second edition), Springer, 1994.

  • Jeremy Avigad. Mathematical Logic and Computation, Cambridge University Press, 2022.

  • Hinman, Peter G. Fundamentals of Mathematical Logic,  A K PETERS, 2005.

Introduction to Computability Theory

  • N.J.Cutland. Computability: an introduction to recursive function theory. Cambridge University press, 1980.

  • Rogers, Hartley; Rogers, H. Theory of Recursive Functions and Effective Computability, MIT Press, 1987.

  • Robič, Borut. The Foundations of Computability Theory, Springer, 2016.

Introduction to Set Theory

  • K. Hrbacek, and T. Jech. Introduction to Set Theory, New York: Marcel Dekker, Inc,  1999.

  • K. Kunen. Set Theory, An Introduction to Independence Proofs, Amsterdam: North-Holland, 1980.

  • T. Jech. Set theory, 3d Edition, New York: Springer，2003.

  • A. Kanamori. The Higher Infinite, Second Edition. Springer Monographs in Mathematics, New York: Springer， 2003.

Introduction to Model Theory

  • Chen Chung Chang and H. Jerome Keisler.  Model Theory. Studies in Logic and the Foundations of Mathematics (3rd ed.). Elsevier,  (1990) [1973].

  • Slomson, A. B.; Bell, J. L.  Models and Ultraproducts: An Introduction. Dover Publications, 2006.

Introduction to Proof Theory

  • Paolo Mancosu, Sergio Galvan, and Richard Zach. An Introduction to Proof Theory: Normalization, Cut-elimination, and Consistency Proofs. Oxford: Oxford University Press, 2021.

  • Wolfram Pohlers. Proof Theory: The First Step into Impredicativity,  Springer, 2008.

  • Gaisi Takeuti. Proof theory (Second edition). Studies in logic and the foundations of mathematics, vol. 81. North-Holland, Amsterdam etc. 1987.

  • Helmut Schwichtenberg and Stanley S. Wainer. Proofs and Computations. In Perspectives in Logic, Cambridge UniversityPress, 2011.

  • John Stillwell, Reverse Mathematics: Proofs from the Inside Out,  Princeton University Press, 2019.

Topics on Gödel’s Incompleteness Theorem

  • R. Murawski. Recursive Functions and Metamathematics: Problems of Completeness and Decidability, Gödel's Theorems. Dordrecht: Kluwer，1999.

  • Per Lindström.  Aspects of Incompleteness, Lecture Notes in Logic v. 10，1997.

  • Raymond M.Smullyan. Gödel’s Incompleteness Theorems, Oxford University Press, 1992.

Topics on Metamathematics of Peano Arithmetic

  • P. Hájek  and P. Pudlák.  Metamathematics of First-Order Arithmetic, Berlin: Springer, 1993.

  • Richard Kaye. Models of Peano Arithmetic, Oxford Logic Guides, Oxford: Oxford University Press，1991.

  • Raymond M.Smullyan. Recursion Theory for Meta-Mathematics, Oxford University Press,1993.

Philosophy of Mathematics and Logic

  • Hamkins, Joel David. Lectures on the Philosophy of Mathematics, MIT Press, 2021.

  • Shapiro, Stewart. Thinking about Mathematics: The Philosophy of Mathematics, Oxford University Press, 2000.

  • Solomon Feferman, John W. Dawson Jr, Warren Goldfarb, Charles Parsons and Wilfried Sieg. Kurt Gödel: Collected Works: Volume I-V, Oxford University Press, USA, 1986-2013.

  • Shapiro, Stewart，The Oxford Handbook of Philosophy of Mathematics and Logic，Oxford University Press, 2007.

  • H. G. Dales and G. Oliveri. Truth in mathematics, Clarendon Press; Oxford University Press 1998.