Selective ultrafilters and 𝜔→(𝜔)^{𝜔}

Eisworth, Todd

doi:10.1090/S0002-9939-99-04835-2

Selective ultrafilters and $\omega \rightarrow (\omega )^\omega$
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Proc. Amer. Math. Soc. 127 (1999), 3067-3071 Request permission

Abstract:

Mathias (Happy families, Ann. Math. Logic. 12 (1977), 59–111) proved that, assuming the existence of a Mahlo cardinal, it is consistent that CH holds and every set of reals in $L(\mathbb {R})$ is $\mathcal {U}$-Ramsey with respect to every selective ultrafilter $\mathcal {U}$. In this paper, we show that the large cardinal assumption cannot be weakened.

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