
doi: 10.1007/bf02122678
Simultaneous generalizations of Ramsey's theorem and single dimension Ramsey-type theorems are proved using ultrafilters on the set N of natural numbers which have certain special properties. The main result utilizes a ``combinatorically large ultrafilter'' to obtain a very strong generalization of Ramsey's theorem and Van der Waerden's theorem. Examples are given to show directions in which these results can be extended.
Combinatorial aspects of partitions of integers, Ramsey's theorem, ultrafilters
Combinatorial aspects of partitions of integers, Ramsey's theorem, ultrafilters
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