论文信息 - Ramsey algebras

Ramsey algebras

Hindman’s theorem says that every finite coloring of the natural numbers has a monochromatic set of finite sums. Ramsey algebras are structures that satisfy an analogue of Hindman’s theorem. The main purpose of this paper is to introduce Ramsey algebras and to present some basic results of their theory. In particular, we show that every infinite integral domain is not a Ramsey algebra.

Wen Chean Teh

[1] Stevo Todorcevic,et al. Introduction to Ramsey Spaces (AM-174) , 2010 .

[2] Miroslav Katětov,et al. A theorem on mappings , 1967 .

[3] Timothy J. Carlson,et al. Some unifying principles in Ramsey theory , 1988, Discret. Math..

[4] A. Hales,et al. Regularity and Positional Games , 1963 .

[5] Neil Hindman,et al. Algebra in the Stone-Cech Compactification: Theory and Applications , 1998 .

[6] Erik Ellentuck,et al. A new proof that analytic sets are Ramsey , 1974, Journal of Symbolic Logic.

[7] Fred Galvin,et al. Borel sets and Ramsey's theorem , 1973, Journal of Symbolic Logic.

[8] Neil Hindman,et al. Finite Sums from Sequences Within Cells of a Partition of N , 1974, J. Comb. Theory, Ser. A.

[9] Stevo Todorcevic,et al. Introduction to Ramsey Spaces , 2010 .

[10] W. Comfort,et al. Ultrafilters: Some old and some new results , 1977 .

[11] Neil Hindman,et al. Ultrafilters and combinatorial number theory , 1979 .

[12] Simultaneous idempotents in _{} and finite sums and products in , 1979 .

[13] J. D. Halpern,et al. A partition theorem , 1966 .

[14] Stephen G. Simpson,et al. A Dual Form of Ramsey's Theorem , 1984 .