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Open Problems in Mathematical Logic

Published 27 Aug 2026 in math.LO | (2608.26628v1)

Abstract: These open problems were presented in the Problem Sessions held during the Tianyuan Workshop on Definability and Computation, June 22-26, 2026. The problems are organized into sections named after their contributors, in the order of their presentations during the workshop. Notes were taken and compiled by Wei Dai, Xiangxi Hu, Yingying Jiang, Ruiwen Li, Tianhao Wang, Xu Wang, and Jie Zou.

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Open Problems

  1. Combining chains of random reals 
  2. Random-chain representation of measure-one ideals 
  3. Combining chains of random reals 
  4. Jumps of comparable 2-random reals 
  5. 2-randoms with bounded complexity difference 
  6. 2-random ideal with no relative randomness 
  7. Jumps of 2-random reals 
  8. Existence of injective one-way real functions (Levin framework) 
  9. Profinite nature of Out(G) for all oligomorphic groups 
  10. Strong jump traceability versus LR-reducibility 
  11. Pi-one class with maximally almost disjoint recursive members 
  12. Fourth-level quantifier-pattern classification 
  13. Deciding reducibility of quantifier patterns 
  14. Realizability degrees of partial-order obstructions 
  15. Kakeya set with high Turing join 
  16. Minimal Kakeya subset 
  17. Borel n-point sets in the plane for fixed n ≥ 2 
  18. Borel algebraically closed extensions 
  19. Choice and bases of vector spaces 
  20. ZFC counterexamples to Marstrand’s projection theorem 
  21. Forcing extensions characterized by finite agreement 
  22. Forcing extensions characterized by finite agreement 
  23. Forcing extensions characterized by finite agreement 
  24. LR-degree intermediate-value question 
  25. Strong nesting characterization of Pi-one-three-MI 
  26. Borel maximal finitely periodic groups 
  27. Intermediate Borel complexity of model isomorphism 
  28. Even Number Game for k at least four 
  29. Recursion-theoretic proof of the Velickovic-Woodin theorem 
  30. Generalized Velickovic-Woodin hypothesis 
  31. Reverse mathematics of positive-tree perfectness 
  32. Dimension analogues of positive-tree principles 
  33. Finitary Ramsey implications 
  34. Generalized pigeonhole principle versus two-randomness 
  35. Unsolvable word problem for Pi groups 
  36. Residually finite non-effectively-residually-finite Pi group 
  37. Hausdorff dimensions of finitely generated profinite groups 
  38. Complexity of first-order properties of profinite groups 
  39. Smoothness of isomorphism for all oligomorphic groups 
  40. Profinite nature of Out(G) for all oligomorphic groups 
  41. Reversibility of computability implications 
  42. Degree of decidable categoricity 
  43. Diagonal degrees for computably enumerable equivalence relations 
  44. Computable copies of compact left-c.e. Polish spaces 
  45. Topologically computably categorical Polish space 
  46. Degree of categoricity for Baire space 
  47. c.e. degrees as topological categoricity degrees 
  48. Definable choice in nonstandard models 
  49. Definable B-sigma-two path 
  50. The Hyperfinite-over-Hyperfinite Problem: Are hyperfinite-over-hyperfinite Borel equivalence relations hyperfinite? 
  51. Undecidability of hyperfiniteness complexity 
  52. Weiss hyperfiniteness for amenable groups 
  53. Uniform subexponential-growth graph hyperfiniteness 
  54. Measurable perfect matching complexity 
  55. Square roots of measure-preserving automorphisms 
  56. Mixing orbit-equivalent action 
  57. Mixing orbit-equivalent action 
  58. Closed I-MED families for Borel ideals 
  59. Closed I-MED families for maximal ideals 

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