Recently, nonstandard methods have been successfully applied in many areas of combinatorics. The nonstandard methodology provides an extension of the universe of mathematics by new ideal (nonstandard) objects such as "an infinitely large natural number", "an infinitely small neighborhood of a point", and many more. The rich structure of relations between the original (standard) and the new (nonstandard) objects enables the standard objects and their standard properties to be described and studied by means of nonstandard concepts. It turns out that this nonstandard description is in many cases more elegant and the nonstandard proofs clearer and shorter than their standard alternatives.
In this series of two talks, I outline a nonstandard approach to Ramsey-type combinatorics. I prove two nonstandard Ramsey-type principles of the following common form (vaguely):
"If, in a coloring of finite subsets of natural numbers, certain nonstandard object (a witness)...

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