论文信息 - Ramsey Algebras and Formal Orderly Terms

Ramsey Algebras and Formal Orderly Terms

Hindman’s theorem says that every finite coloring of the natural numbers has a monochromatic set of finite sums. A Ramsey algebra is a structure that satisfies an analogue of Hindman’s theorem. In this paper, we present the basic notions of Ramsey algebras by using terminology from mathematical logic. We also present some results regarding classification of Ramsey algebras.

Wen Chean Teh

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

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

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

[4] Wen Chean. RAMSEY ALGEBRAS AND STRONGLY REDUCTIBLE ULTRAFILTERS , 2013 .

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

[6] Wen Chean Teh. Ramsey algebras , 2016, J. Math. Log..

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

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

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

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

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

[12] Herbert B. Enderton,et al. A mathematical introduction to logic , 1972 .

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