Sh:564

• Shelah, S. (1996). Finite canonization. Comment. Math. Univ. Carolin., 37(3), 445–456. arXiv: math/9509229 MR: 1426909
• Abstract:
  The canonization theorem says that for given m,n for some m^* (the first one is called ER(n;m)) we have: for every function f with domain [{1,\ldots,m^*}]^n, for some A\in [{1,\ldots,m^*}]^m, the question of when the equality f({i_1,\ldots,i_n})=f({j_1,\ldots,j_n}) (where i_1<\ldots<i_n and j_1 <\ldots< j_n are from A) holds has the simplest answer: for some v \subseteq \{1,\ldots,n\} the equality holds iff (\forall\ell\in v)(i_\ell = j_\ell).

  In this paper we improve the bound on ER(n,m) so that fixing n the number of exponentiation needed to calculate ER(n,m) is best possible.

• published version (12p)

@article{Sh:564,
 author = {Shelah, Saharon},
 title = {{Finite canonization}},
 journal = {Comment. Math. Univ. Carolin.},
 fjournal = {Commentationes Mathematicae Universitatis Carolinae},
 volume = {37},
 number = {3},
 year = {1996},
 pages = {445--456},
 issn = {0010-2628},
 mrnumber = {1426909},
 mrclass = {05D10},
 note = {\href{https://arxiv.org/abs/math/9509229}{arXiv: math/9509229}},
 arxiv_number = {math/9509229}
}