The varieties of arboreal experience

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

First, let me simply update the references to my column on the Paris-Harrington Theorem: The papers of Erdös and Mills and of Ketonen and Solovay have since appeared, the former in the Journal of Combinatorial Theory, series A, vol. 30 (1981), pp. 53–70, and the latter in the Annals of Mathematics, vol. 113 (1981), pp. 267- 314. In addition, I note the bookRamsey Theory (J. Wiley, 1980) by R. Graham, B. Rothschild and J. Spencer has a nice exposition of a variant of the Ketonen-Solovay work.
Article Google Scholar
Friedman’s work reported above is not, at the time of writing, in manuscript form and I can only cite some background material. With respect to Kruskal’s Theorem and ordinals, I suggest: J. B. Kruskal, Well-quasi-ordering, the tree theorem, and Vázsonyi’s conjecture, Trans. AMS 95 (1960), pp. 210–225.
Article MATH MathSciNet Google Scholar
C. St. J. A. Nash-Williams, On well-quasi-ordering finite trees, Proc. Cambridge Phil. Soc. 59 (1963), pp. 833–835.
Article MATH MathSciNet Google Scholar
D. Schmidt, Well-partial-orderings and their maximal order types, Habilitationsschrift, Heidelberg, 1978.
Google Scholar
Finally, a good reference on Γ₀, ordinals, and proof theory is K. Schütte,Proof Theory (Springer-Verlag, 1977).

Dept. of Mathematics, Ohio State University, 43210, Columbus, Ohio, USA
C. Smoryński

Authors

C. Smoryński
View author publications
You can also search for this author in PubMed Google Scholar

Smoryński, C. The varieties of arboreal experience. The Mathematical Intelligencer 4, 182–189 (1982). https://doi.org/10.1007/BF03023553

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.