List of Recent Publications

 

1. C. T. Chong and Yue Yang, $\Sigma_2$ induction and infinite injury priority arguments. Part I: Maximal sets and the jump operator. J. Symbolic Logic, 63 (1998), 797-814

2. C. T. Chong and Yue Yang, $\Sigma_2$ induction and infinite injury priority arguments. Part II: Tame $\Sigma_2$ coding and the jump operator. Annals of Pure and Applied Logic 87 (1997), 103-116

3. C. T. Chong and Yue Yang, Recursion theory in weak fragments of arithmetic: A study of cuts. In: Proc. Sixth Asian Logic Conference, Beijing, pp. 47-65, World Scientific, 1998

4. C. T. Chong and Sy D. Friedman, Ordinal recursion theory, in: Handbook of Computability Theory, pp. 277-300, Studies in Logic and Foundations of Mathematics, Elsevier, 1999

5. C. T. Chong, L. Qian and Yue Yang, The Friedberg Jump Inversion Theorem revisited: A study of undefinable cuts, in: Logic Colloquium 98, pp. 140-153, Association for Symbolic Logic, 2000

6. C. T. Chong and Yue Yang, Computability theory in arithmetic: Provability, structure and techniques, in: Computability Theory and Its Applications, pp. 73-81, Contemporary Math. 257, Amer. Math. Soc., 2000

7. C. T. Chong, L. Qian. T. A. Slaman and Yue Yang, $\Sigma_2$ induction and infinite injury priority arguments. Part III: Prompt sets, minimal pairs and Shoenfields conjecture, Israel J. Math. 121 (2001), 1-28

8. C. T. Chong, R. A. Shore and Yue Yang, Interpreting arithmetic in models of $\Sigma_4$ induction, in: Reverse Mathematics 2001 (Stephen Simpson, Ed.). Wellesley, MA: A K Peters; Urbana, IL: Association for Symbolic Logic (ASL) (ISBN 1-56881-263-9/hbk; 1-56881-264-7/pbk). Lecture Notes in Logic 21, 120-146 (2005)

9. M. M. Arslanov, C. T. Chong,  S. B. Cooper and Yue Yang, The Minimal E-degree Problem in Fragments of Peano Arithmetic, Annals of Pure and Applied Logic 131 (2005), 159-175

10. C. T. Chong, Ansheng Li and Yue Yang, The existence of high nonbounding degrees in the difference hierarchy, Annals of Pure and Applied Logic, 138, No. 1-3, 31-51 (2006)

11. C. T. Chong, Ansheng Li and Yue Yang, The difference hierarchy in models of $\De;ta_1$ induction

12. C. T. Chong and Yue Yang, The jump of a $\Sigma\sb n$-cut, J. Lond. Math. Soc. (2) 75 (2007), no.3, 690--704. 03D20 (03F30 03H15)

13. C. T. Chong, Nonstandard methods in Ramsey's Theorem for pairs, in: Computational prospects of infinity. Part II: Presented talks. Selected papers of the workshop, June 20-August 15, 2005 (Chitat Chong, Qi Feng, Theodoare A. Slaman, W. Hugh Woodin and Yue Yang, Eds.). Hackensack, NJ: World Scientific (ISBN 978-981-279-654-7/hbk). Lecture Notes Series. Institute for Mathematical Sciences. National University of Singapore 15, 47-57 (2008)

14. C. T. Chong, Andre Nies and Liang Yu, Higher randomness notions and their lowness properties, Israel Journal of Mathematics, 166, 39-60 (2008)

15. C. T. Chong and Liang Yu, Maximal chains in the Turing degrees, J. Symbolic Logic 72 (2007), no. 4, 1219--1227. 03D28 (03E25 03E35 03E45)

16. C. T. Chong and Liang Yu, Thin Pi^1_1 maximal antichains in the Turing degrees, in: Barry S Cooper, Benedikt Lowe and Andrea Sorbi (Editors), CIE 2007, Springer Lecture Notes in Computer Science Vol. 1497, pp. 162--168, 2007.

17. C. T. Chong and Liang Yu, A$\Pi^1_1$ uniformization principle for reals, Transactions of American Mathematical Society, 361 (2009), 4233-4245

18. C. T. Chong and Wei Wang, Hyperimmune free degrees beyond $\omega$

19. C. T. Chong, Wei Wang and Liang Yu, The consistency strength of projective Martin's Conjecture, Fundamenta Mathematicae 207 (2010), 21--27

20. C. T. Chong, Steffen Lempp and Yue Yang, On the role of the collection principle for \Sigma^0_2 formulas in second order reverse mathematics, Proceedings of the American Mathematical Society 138 (2010), 1093--1100

21. C. T. Chong and Theodore A. Slaman, The theory of $\alpha$-degrees is undecidable, Israel J. Math., 189 (2010), 229--252

22. C. T. Chong, Theodore A Slaman and Yue Yang, $\Pi^1_1$-conservation of combinatorial principles weaker than Ramsey's theorem for pairs, Advances in Mathematics, 230 (2012), 1060--1077

23. C. T. Chong, Theodore A. Slaman and Yue Yang, The metamathematics of Stable Ramsey's Theorem for pairs, Journal of the American Mathematical Society, 27 (2014), 863--892.

24. C. T Chong and Liang Yu, Randomness in the higher setting, Journal of Symbolic Logic 80 (2015), 1131-1148

25. C. T. Chong, Wei Li and Yue Yang, Nonstandard models in recursion theory and reverse mathematics, Bulletin of Symbolic Logic 20 (2014), 170-200

26. C. T. Chong, Gordon Hoi, Frank Stephan and Daniel Turetsky, Partial functions and domination, Logical Methods in Computer Science, 11(2015), 1-16

27. C. T. Chong and Liang Yu, Measure-theoretic applications of higher Demuth randomness, Transactions of the American Mathematical Society 328 (2016), 8249-8265

28. C. T. Chong, Theodore A. Slaman and Yue Yang, The inductive strength of Ramsey's Theorem for pairs, Advances in Mathematics , 21 (2017), 121-141

29. C. T. Chong, $1$-generic degrees bounding minimal degrees revisited, Lecture Notes in Computer Science, to appear (Rod Downey Festschrift)