Archive for Mathematical Logic 41 (7):619-630 (2002)

Let X be an infinite internal set in an ω1-saturated nonstandard universe. Then for any coloring of [X] k , such that the equivalence E of having the same color is countably determined and there is no infinite internal subset of [X] k with all its elements of different colors (i.e., E is condensating on X), there exists an infinite internal set Z⊆X such that all the sets in [Z] k have the same color. This Ramsey-type result is obtained as a consequence of a more general one, asserting the existence of infinite internal Q-homogeneous sets for certain Q ⊆ [[X] k ] m , with arbitrary standard k≥ 1, m≥ 2. In the course of the proof certain minimal condensating countably determined sets will be described
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DOI 10.1007/s001530100129
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Standard Foundations for Nonstandard Analysis.David Ballard & Karel Hrbacek - 1992 - Journal of Symbolic Logic 57 (2):741-748.
Internal Set Theory: A New Approach to Nonstandard Analysis.Edward Nelson - 1977 - Journal of Symbolic Logic 48 (4):1203-1204.

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