Problem List of Andreas Weiermann

Conceptual Problems

  • The natural well ordering problem More details.
  • The classification problem for the recursive functions
  • Threshold classifications for independence results
  • Limit laws for ordinals
  • Transfer between analytic number theory and ordinal notations
  • Natural coding of ordinals

    • Concrete Problems

  • Give a threshold classification of the impredicative Ramsey theorem
  • Enumeration theory for the Howard Bachmann ordinal
  • A sharp wpo characterization of the Howard Bachmann ordinal
  • Multiplicative codings of ordinals below epsilon_0 have slowly varying count functions
  • Additive codings of ordinals below epsilon_0 are in the Compton class RT_0
  • Skolem's problem on describing epsilon_0 (or a slightly bigger ordinal) in terms of plus, times and exponentiation
  • Does RT^2_2 prove the totality of the Ackermann function? (From Cholak, Jockusch and Slaman's JSL paper.)
  • A bunch of problems on braid groups found in the work by Dehornoy et al.

    • Problem posed by Harvey Friedman

    (Let N^k the set of k-tuples of elements from N. Identify a natural number with its set of predecessors.) Investigate the phase transition for the following assertion
    For every k,c,p there exists N so large that for every F:N^k --> c there exists A contained in N such that card(A)=p and card F[A^k]\leq number of order types in k^k. Replace otype(k^k) by p^k or by f(k) or by f(p,k). Consider the assertion with f-largeness condition and f-regressiveness. Classify the corresponding principles from Finite functions and the necessary use of large cardinals (Annals of Mathematics 148 (1998) 803-893 similarly.