# Publications

*Books*

2. Chi Tat Chong and Liang Yu, *Recursion Theory: Computational Aspects of Definability*, Logic and Its Applications Volume 8, de Gruyter, 2015 [URL]

1. C. T. Chong. *Techniques of Admissible Recursion Theory*, Lecture Notes in Mathematics Volume 1106, Springer Verlag, 1984

* *

# Research Papers

65. Chi Tat Chong, Wei Wang and Yue Yang, Conservation strength of the infinite pigeonhole principle for trees, arkiv

64. Chi Tat Chong, Wei Li, Lu Liu and Yue Yang, The strength of Ramsey’s Theorem for Pairs over trees: I. Weak K\”onig’s Lemma, *Transactions of the American Mathematical Society*, to appear * [PDF]*

63. Chi Tat Chong, Ramsey’s Theorem for pairs in reverse mathematics,* Preprint PDF
*

* *62. David Belanger, Chi Tat Chong, Wei Wang Tin Lok Wong and Yue Yang, Where Pigeonhole Principles Meet K\”onig Lemmas, *Transactions of the American Mathematical Society*, to appear* [PDF]
*

61. C. T. Chong, Wei Li, Wei Wang and Yue Yang, On the strength of Ramsey’s Theorem for trees, *Advances in* Mathematics, 369 (2020), 1071780 *[Postcript]*

60. C. T. Chong, Wei Li, Wei Wang and Yue Yang, On the computability of perfect subsets of sets of positive measure, *Proceedings of the American Mathematical Society*, 147 (2019), 4021-4028

59. C. T. Chong, Liu Zhen Wu and Liang Yu, Basis theorems for $\Sigma^1_2$-sets, *Journal of Symbolic Logic*, 84 (2019), 376–387

58. C. T. Chong, $1$-generic degrees bounding minimal degrees revisited, in: *Computability and* Complexity*: Essays Dedicated to Rodney G. Downey on the Occasion of His 60th Birthday*, Lecture Notes in Computer Science Volume 10010, pp. 536–546, Springer 2017

57. 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

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

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

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

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

52. 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.

51. 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

50. C. T. Chong and Theodore A. Slaman, The theory of $\alpha$-degrees is undecidable, *Israel Journal of Mathematics* 189 (2010), 229–252

49. 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

48. C. T. Chong, Wei Wang and Liang Yu, The consistency strength of projective Martin’s Conjecture,* Fundamenta Mathematicae* 207 (2010), 21–27

47. C. T. Chong and Wei Wang, Hyperimmune free degrees beyond $\omega$, *Unpublished notes*

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

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

44. 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, *Institute for Mathematical Sciences Lecture Notes Volume 15, pp. 47–57, World Scientific, 200

43. C. T. Chong and Liang Yu, Thin Pi^1_1 maximal antichains in the Turing degrees, in: *CIE 2007*, Lecture Notes in Computer Science Volume 1497, pp. 162–168, Springer 2007.

42. C. T. Chong and Liang Yu, Maximal chains in the Turing degrees, *Journal of Symbolic Logic* 72 (2007), no. 4, 1219–1227. 03D28 (03E25 03E35 03E45)

41. C. T. Chong and Yue Yang, The jump of a $\Sigma\sb n$-cut, *Journal of the London Mathematical Society* 75 (2007), 690–704

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

39. 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

38. C. T. Chong, R. A. Shore and Yue Yang, Interpreting arithmetic in models of $\Sigma_4$ induction, in: *Reverse Mathematics 2001,* Association for Symbolic Logic Lecture Notes in Logic Volume 21, pp. 120–146, A K Peters, 2005

37. 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 Journal of Mathematics *121 (2001), 1–28

36. C. T. Chong and Yue Yang, Computability theory in arithmetic: Provability, structure and techniques, in: *Computability Theory and* *Its Applications*, pp. 73–81, Contemporary Mathematics Volume 257, Amer. Mathematical Society, 2000

35. 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

34. 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

33. C. T. Chong and Yue Yang, Recursion theory in weak fragments of arithmetic: A study of cuts. In: Proceedings of the Sixth Asian *Logic Conference 1996*, Beijing, pp. 47–65, World Scientific, 1998

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

31. 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

30. C. T. Chong, The polynomial topological complexity of Fatou-Julia sets, *Advances in Computational Mathematics* 3 (1995), 369–371

29. C. T. Chong, Positive reducibility of the interior of filled Julia sets, *Journal of Complexity *10 (1994), 437–441

28. C. T. Chong and K. J. Mourad, $\Sigma_n$-definable sets without $\Sigma_n$-induction, *Transactions of the American Mathematical Society* 334 (1992), 349–363

27. C. T. Chong and Rodney G. Downey, Minimal degrees recursive in $1$-generic degrees, *Annals of Pure and Applied Logic *48 (1990), 215–2250

26. C. T. Chong and K. J. Mourad, Positive solutions to Post’s problem, in: *Recursion Theory Week: Proceedings of a Conference Held in Oberwolfach*, pp. 33–40, Lecture Notes in Mathematics Volume 1432, Springer Verlag, 1990

25. C. T. Chong and K. J. Mourad, The degree of a $\Sigma_n$-cut, *Annals of Pure and Applied Logic 48 (1990), 227–235*

24. C. T. Chong and Rod ey G. Downey, Degrees bounding minimal degrees, *Mathematical Proceedings of the Cambridge Philosophical Society *105 (1989), 211–222

23. C. T. Chong, Hyperhypersimple sets and $\Delta_2$ systems, *Annals of Pure and Applied Logic 44 (1989), 25–38*

22. C. T. Chong, Maximal sets and fragments of Peano arithmetic, *Nagoya Mathematical Journal* 115 (1989), 165–183

21. C. T. Chong, Recursively enumerable sets in models of $\Sigma_2$-collection, in: *Mathematical Logic and Its Applications, Proceedings of a Conference Held in Kyoto, *pp. 1–15 , Lecture Notes in Mathematics Volume 1388, Springer Verlag, 1989

20. C. T. Chong, $\Sigma_2$-collection and maximal sets, in: *Research Institute of Mathematical Sciences *Volume 644, pp. 4–15, Kyoto University, 1988

19. C. T. Chong, Degree-theoretic bounds on the Morley rank, *Archive for Mathematical Logic* 26 (1987), 137–145

18. C. T. Chong, $\Sigma_1$-density and Turing degree, *Mathematical Logic Quarterly *33 (1987), 141–145

17. C. T. Chong, $1$-generic degrees and minimal degrees in higher recursion theory, *Japanese Journal of Mathematics* 13 (1987), 381–392

16. C. T. Chong, Recursion theory on strongly $\Sigma_2$-inadmissible ordinals, in: *Recursion Theory Week: Proceedings of a Conference Held in Oberwolfach*, pp. 49–64, Springer Verlag 1985

15. C. T. Chong and Carl G. Jockusch, Minimal degrees and $1$-generic sets below $0’$, in: *Computation and Proof Theory, Proceedings of Logic Colloquium ’83*, Lecture Notes in Mathematics Volume 1104, pp. 63–77, Springer Verlag, 1984

14. C. T. Chong, Minimal $\alpha$-hyperdegrees, *Archive for Mathematical Logic* 24 (1984), 63–71

13. C. T. Chong and Sy D. Friedman, Degree theory on $\aleph_\omega$, *Annals of Pure and Applied Logic* 24 (1983), 87–97

12. C. T. Chong, Hyperhypersimple superset in admissible recursion theory, *Journal of Symbolic Logic* 48 (1983), 185–192

11. C. T. Chong, Global and local admissibility: II. Major subsets and automorphisms, *Annals of Pure and Applied Logic* 24 (1983), 99–111

10. C. T. Chong, Double jumps of minimal degrees over cardinals, *Journal of Symbolic Logic* 47 (1982), 329–334

9. C. T. Chong, Global and local admissibility, in: *Proceedings of the Logic Colloquium ’80*, Studies in Logic and the Foundations of Mathematics Volume 109, pp. 325–338, North Holland, 1982

8. C. T. Chong, Rich sets, *Proceedings of the American Mathematical Society* 80 (1980), 458–460

7. C. T. Chong, Generic sets and minimal $\alpha$-degrees, *Transactions of the American Mathematical Society *254 (1979), 157–169

6. C. T. Chong, Major subsets of $\alpha$-recursively enumerable set, *Israel Journal of Mathematics *34 (1979), 106–114

5. C. T. Chong, A recursion-theoretic characterization of constructible reals, *Bulletin of the London Mathematical Society* 9 (1977), 241–244

4. C. T. Chong and Manuel Lerman, Hyperhypersimple $\alpha$-r.e. sets, *Annals of Mathe4matical Logic* 9 (1976), 1–48

3. C. T. Chong, Minimal upper bounds for ascending sequences of $\alpha$-recursively enumerable degrees, *Journal of Symbolic Logic *41 (1976), 250–260

2. C. T. Chong, An $\alpha$-finite injury method of the unbounded type, *Journal of Symbolic Logic* 41 (1976), 1–17

1. C. T. Chong, Almost local non-$\alpha$-recursiveness, *Journal of Symbolic Logic* 39 (1974), *552–62*

### Other Articles (Selected)

3. Chong Chi Tat, Fifty years of mathematics in Singapore: A personal perspective, in: *50 Years of Science in Singapore, *pp. 105–118, World Scientific, 2015

2. Chi Tat Chong and Yue Yang, An interview with Gerald Sacks, in: Chi Tat Chong and Liang Yu, *Recursion Theory: Computational Aspects of Definability*, pp. 275–292

1. C. T. Chong and Y. K. Leong, An interview with Jean-Pierre Serre, *Mathematical Medley *13 (1985), 11-19; reprinted in *Mathematical Intelligencer* 8 (1986), 8–13