# Ramsey's Theorem

Formalized Mathematics (2008)

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

## Access Full Article

top## Abstract

top## How to cite

topMarco 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

top- [1] M. Aigner and G. M. Ziegler. Proofs from THE BOOK. Springer-Verlag, Berlin Heidelberg New York, 2004. Zbl1098.00001
- [2] Grzegorz Bancerek. Cardinal numbers. Formalized Mathematics, 1(2):377-382, 1990.
- [3] Grzegorz Bancerek and Krzysztof Hryniewiecki. Segments of natural numbers and finite sequences. Formalized Mathematics, 1(1):107-114, 1990.
- [4] Czesław Byliński. Functions and their basic properties. Formalized Mathematics, 1(1):55-65, 1990.
- [5] Czesław Byliński. Functions from a set to a set. Formalized Mathematics, 1(1):153-164, 1990.
- [6] Czesław Byliński. Partial functions. Formalized Mathematics, 1(2):357-367, 1990.
- [7] Agata Darmochwał. Finite sets. Formalized Mathematics, 1(1):165-167, 1990.
- [8] Krzysztof Hryniewiecki. Basic properties of real numbers. Formalized Mathematics, 1(1):35-40, 1990.
- [9] T. J. Jech. Set Theory. Springer-Verlag, Berlin Heidelberg New York, 2002. Zbl0419.03028
- [10] Rafał Kwiatek. Factorial and Newton coefficients. Formalized Mathematics, 1(5):887-890, 1990.
- [11] Takaya Nishiyama and Yasuho Mizuhara. Binary arithmetics. Formalized Mathematics, 4(1):83-86, 1993.
- [12] Konrad Raczkowski and Paweł Sadowski. Equivalence relations and classes of abstraction. Formalized Mathematics, 1(3):441-444, 1990.
- [13] Marco Riccardi. The sylow theorems. Formalized Mathematics, 15(3):159-165, 2007.
- [14] Andrzej Trybulec. A Borsuk theorem on homotopy types. Formalized Mathematics, 2(4):535-545, 1991.
- [15] Zinaida Trybulec. Properties of subsets. Formalized Mathematics, 1(1):67-71, 1990.
- [16] Edmund Woronowicz. Relations and their basic properties. Formalized Mathematics, 1(1):73-83, 1990.
- [17] Edmund Woronowicz. Relations defined on sets. Formalized Mathematics, 1(1):181-186, 1990.

## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.