Tukey reductions of nowhere Ramsey to Silver null sets

Spinas, Otmar

doi:10.1090/proc/15869

Tukey reductions of nowhere Ramsey to Silver null sets
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Proc. Amer. Math. Soc. 150 (2022), 2715-2727 Request permission

Abstract:

We prove that the ideal of nowhere Ramsey sets is Tukey reducible to each of the finite-dimensional Silver null ideals. This is in line with an earlier result of the author [Israel J. Math. 211 (2016), pp. 473–480] that the meager ideal is Tukey reducible to the Silver null ideal, and it answers two questions asked by Spinas and Wohofsky [Fund. Math. 254 (2021), pp. 261–303].

We also show that if the homogeneity number $\mathfrak {hm}$ equals $2^{\aleph _0}$, then the additivity of the Marczewski ideal is below the $\sigma$-splitting number $\mathfrak {s_\sigma }$.

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