论文信息 - Ultrafilters and multidimensional Ramsey Theorems

Ultrafilters and multidimensional Ramsey Theorems

Utilizing ultrafilters on the setN of natural numbers which have certain special properties, we prove some simultaneous generalizations of Ramsey's Theorem and several single dimension Ramsey-type theorems. (For instance, as a very special case, we obtain a simultaneous generalization of Ramsey's Theorem and van der Waerden's Theorem.) Examples are given to show directions in which these results cannot be extended.

Neil Hindman | Vitaly Bergelson

[1] W. Wistar Comfort,et al. Some recent applications of ultrafilters to topology , 1977 .

[2] Alan D. Taylor,et al. A Canonical Partition Relation for Finite Subsets of omega , 1976, J. Comb. Theory, Ser. A.

[3] J. Spencer. Ramsey Theory , 1990 .

[4] Neil Hindman. Partitions and Sums and Products - Two Counterexamples , 1980, J. Comb. Theory, Ser. A.

[5] Neil Hindman,et al. A combinatorially large cell of a partition of N , 1988, J. Comb. Theory, Ser. A.

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

[7] Keith R. Milliken,et al. Ramsey's Theorem with Sums or Unions , 1975, J. Comb. Theory, Ser. A.

[8] Neil Hindman,et al. Density versions of two generalizations of Schur's theorem , 1988, J. Comb. Theory, Ser. A.