Ramsey's Theorem

Marco Riccardi

Formalized Mathematics (2008)

  • Volume: 16, Issue: 2, page 203-205
  • ISSN: 1426-2630

Abstract

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The goal of this article is to formalize two versions of Ramsey's theorem. The theorems are not phrased in the usually pictorial representation of a coloured graph but use a set-theoretic terminology. After some useful lemma, the second section presents a generalization of Ramsey's theorem on infinite set closely following the book [9]. The last section includes the formalization of the theorem in a more known version (see [1]).MML identifier: RAMSEY 1, version: 7.9.01 4.101.1015

How to cite

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Marco Riccardi. "Ramsey's Theorem." Formalized Mathematics 16.2 (2008): 203-205. <http://eudml.org/doc/266950>.

@article{MarcoRiccardi2008,
abstract = {The goal of this article is to formalize two versions of Ramsey's theorem. The theorems are not phrased in the usually pictorial representation of a coloured graph but use a set-theoretic terminology. After some useful lemma, the second section presents a generalization of Ramsey's theorem on infinite set closely following the book [9]. The last section includes the formalization of the theorem in a more known version (see [1]).MML identifier: RAMSEY 1, version: 7.9.01 4.101.1015},
author = {Marco Riccardi},
journal = {Formalized Mathematics},
language = {eng},
number = {2},
pages = {203-205},
title = {Ramsey's Theorem},
url = {http://eudml.org/doc/266950},
volume = {16},
year = {2008},
}

TY - JOUR
AU - Marco Riccardi
TI - Ramsey's Theorem
JO - Formalized Mathematics
PY - 2008
VL - 16
IS - 2
SP - 203
EP - 205
AB - The goal of this article is to formalize two versions of Ramsey's theorem. The theorems are not phrased in the usually pictorial representation of a coloured graph but use a set-theoretic terminology. After some useful lemma, the second section presents a generalization of Ramsey's theorem on infinite set closely following the book [9]. The last section includes the formalization of the theorem in a more known version (see [1]).MML identifier: RAMSEY 1, version: 7.9.01 4.101.1015
LA - eng
UR - http://eudml.org/doc/266950
ER -

References

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  1. [1] M. Aigner and G. M. Ziegler. Proofs from THE BOOK. Springer-Verlag, Berlin Heidelberg New York, 2004. Zbl1098.00001
  2. [2] Grzegorz Bancerek. Cardinal numbers. Formalized Mathematics, 1(2):377-382, 1990. 
  3. [3] Grzegorz Bancerek and Krzysztof Hryniewiecki. Segments of natural numbers and finite sequences. Formalized Mathematics, 1(1):107-114, 1990. 
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  8. [8] Krzysztof Hryniewiecki. Basic properties of real numbers. Formalized Mathematics, 1(1):35-40, 1990. 
  9. [9] T. J. Jech. Set Theory. Springer-Verlag, Berlin Heidelberg New York, 2002. Zbl0419.03028
  10. [10] Rafał Kwiatek. Factorial and Newton coefficients. Formalized Mathematics, 1(5):887-890, 1990. 
  11. [11] Takaya Nishiyama and Yasuho Mizuhara. Binary arithmetics. Formalized Mathematics, 4(1):83-86, 1993. 
  12. [12] Konrad Raczkowski and Paweł Sadowski. Equivalence relations and classes of abstraction. Formalized Mathematics, 1(3):441-444, 1990. 
  13. [13] Marco Riccardi. The sylow theorems. Formalized Mathematics, 15(3):159-165, 2007. 
  14. [14] Andrzej Trybulec. A Borsuk theorem on homotopy types. Formalized Mathematics, 2(4):535-545, 1991. 
  15. [15] Zinaida Trybulec. Properties of subsets. Formalized Mathematics, 1(1):67-71, 1990. 
  16. [16] Edmund Woronowicz. Relations and their basic properties. Formalized Mathematics, 1(1):73-83, 1990. 
  17. [17] Edmund Woronowicz. Relations defined on sets. Formalized Mathematics, 1(1):181-186, 1990. 

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