Finite canonization

Saharon Shelah

Finite canonization

Saharon Shelah^*

^*Corresponding author for this work

Einstein Institute of Mathematics

Research output: Contribution to journal › Article › peer-review

4 Scopus citations

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,.., m*]ⁿ, for some A ∈ [1,.., m*]^m, the question of when the equality f(i₁,.., i_n) = f(j₁,.., j_n) (where i₁ < · · · < i_n and j₁ < · · · jn are from A) holds has the simplest answer: for some v ⊆ (1,.., n) the equality holds iffWe improve the bound on ER(n, m) so that fixing n the number of exponentiation needed to calculate ER(n, m) is best possible.

Original language	English
Pages (from-to)	445-456
Number of pages	12
Journal	Commentationes Mathematicae Universitatis Carolinae
Volume	37
Issue number	3
State	Published - 1996

Bibliographical note

Publisher Copyright:
© 1996, Charles University, Faculty of Mathematics and Physics.

Keywords

Canonization
Erdös-Rado theorem
Ramsey theory

Cite this

@article{5d88565e833f4246a3d57f99b54cb053,

title = "Finite canonization",

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,.., m*]n, for some A ∈ [1,.., m*]m, the question of when the equality f(i1,.., in) = f(j1,.., jn) (where i1 < · · · < in and j1 < · · · jn are from A) holds has the simplest answer: for some v ⊆ (1,.., n) the equality holds iffWe improve the bound on ER(n, m) so that fixing n the number of exponentiation needed to calculate ER(n, m) is best possible.",

keywords = "Canonization, Erd{\"o}s-Rado theorem, Ramsey theory",

author = "Saharon Shelah",

note = "Publisher Copyright: {\textcopyright} 1996, Charles University, Faculty of Mathematics and Physics.",

year = "1996",

language = "אנגלית",

volume = "37",

pages = "445--456",

journal = "Commentationes Mathematicae Universitatis Carolinae",

issn = "0010-2628",

publisher = "Charles University, Faculty of Mathematics and Physics",

number = "3",

}

TY - JOUR

T1 - Finite canonization

AU - Shelah, Saharon

PY - 1996

Y1 - 1996

N2 - 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,.., m*]n, for some A ∈ [1,.., m*]m, the question of when the equality f(i1,.., in) = f(j1,.., jn) (where i1 < · · · < in and j1 < · · · jn are from A) holds has the simplest answer: for some v ⊆ (1,.., n) the equality holds iffWe improve the bound on ER(n, m) so that fixing n the number of exponentiation needed to calculate ER(n, m) is best possible.

AB - 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,.., m*]n, for some A ∈ [1,.., m*]m, the question of when the equality f(i1,.., in) = f(j1,.., jn) (where i1 < · · · < in and j1 < · · · jn are from A) holds has the simplest answer: for some v ⊆ (1,.., n) the equality holds iffWe improve the bound on ER(n, m) so that fixing n the number of exponentiation needed to calculate ER(n, m) is best possible.

KW - Canonization

KW - Erdös-Rado theorem

KW - Ramsey theory

UR - http://www.scopus.com/inward/record.url?scp=0346789618&partnerID=8YFLogxK

M3 - ???researchoutput.researchoutputtypes.contributiontojournal.article???

AN - SCOPUS:0346789618

SN - 0010-2628

VL - 37

SP - 445

EP - 456

JO - Commentationes Mathematicae Universitatis Carolinae

JF - Commentationes Mathematicae Universitatis Carolinae

IS - 3

ER -

Finite canonization

Abstract

Bibliographical note

Keywords

Other files and links

Fingerprint

Cite this