Partition theorems and ultrafilters

Baumgartner, James E.; Taylor, Alan D.

doi:10.1090/S0002-9947-1978-0491193-1

Partition theorems and ultrafilters
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by James E. Baumgartner and Alan D. Taylor

Trans. Amer. Math. Soc. 241 (1978), 283-309

DOI: https://doi.org/10.1090/S0002-9947-1978-0491193-1

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Abstract:

We introduce a class of ultrafilters on $\omega$ called k-arrow ultrafilters and characterized by the partition relation $U \to {(U,k)^2}$. These are studied in conjunction with P-points, Q-points, weakly Ramsey and Ramsey ultrafilters.

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P-points and Ramsey subsets of