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, Computability and Complexity, Lecture Notes in Compuer Science, Springer 2017, (Rod Downey Festschrift)

30. C. T. Chong, Liu Zhen Wu and Liang Yu, Basis theorems for $\Sigma^1_2$-sets, Preprint

31. C. T. Chong, Wei Li, Wei Wang and Yue Yang, On the strength of Ramsey's theorem for trees, Preprint