Ramsey's Theorem
Marco Riccardi
Formalized Mathematics, Tome 16 (2008), p. 203-205 / Harvested from The Polish Digital Mathematics Library
Access to full text
Full (PDF)

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

Publié le : 2008-01-01
EUDML-ID : urn:eudml:doc:266950 
@article{bwmeta1.element.doi-10_2478_v10037-008-0026-y,
     author = {Marco Riccardi},
     title = {Ramsey's Theorem},
     journal = {Formalized Mathematics},
     volume = {16},
     year = {2008},
     pages = {203-205},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_v10037-008-0026-y}
}

Marco Riccardi. Ramsey's Theorem. Formalized Mathematics, Tome 16 (2008) pp. 203-205. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_v10037-008-0026-y/

[1] M. Aigner and G. M. Ziegler. Proofs from THE BOOK. Springer-Verlag, Berlin Heidelberg New York, 2004. | Zbl 1098.00001

[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. | Zbl 0419.03028

[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.