A Classification of Rapidly Growing Ramsey Functions

@inproceedings{Weiermann2003ACO,
  title={A Classification of Rapidly Growing Ramsey Functions},
  author={Andreas Weiermann},
  year={2003}
}
Let f be a number-theoretic function. A finite set X of natural numbers is called f -large if card(X) ≥ f(min(X)). Let PHf be the Paris Harrington statement where we replace the largeness condition by a corresponding f -largeness condition. We classify those functions f for which the statement PHf is independent of first order (Peano) arithmetic PA. If f is a fixed iteration of the binary length function, then PHf is independent. On the other hand PHlog∗ is provable in PA. More precisely let f… CONTINUE READING

From This Paper

Topics from this paper.
22 Citations
22 References
Similar Papers

References

Publications referenced by this paper.
Showing 1-10 of 22 references

On rapidly growing Ramsey functions

  • W. Buchholz
  • Technical report, München
  • 1991
Highly Influential
7 Excerpts

Weiermann : How to characterize provably total functions by the Buchholz operator method

  • B. Blankertz, A.
  • On the slowly well orderedness of ε 0…
  • 2002

Perfect” statements. Posting the FOM email list from 05.02.1999

  • H. Friedman
  • 1999

How to characterize provably total functions by the Buchholz operator method

  • B. Blankertz, A. Weiermann
  • Springer Lecture Notes in Logic
  • 1996
2 Excerpts

A uniform approach to fundamental sequences and hierarchies

  • W. Buchholz, A. Cichon, A. Weiermann
  • Mathematical Logic Quarterly
  • 1994
2 Excerpts

Similar Papers

Loading similar papers…