Strong measure zero sets and rapid filters

Journal of Symbolic Logic 53 (2):393-402 (1988)
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Abstract

We prove that $\operatorname{cons}(ZF)$ implies $\operatorname{cons}(ZF +$ Borel conjecture + there exists a Ramsey ultrafilter). We also prove some results on strong measure zero sets from the existence of generalized Luzin sets. We study the relationships between strong measure zero sets and rapid filters on ω

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10.2307/2274512

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Citations of this work

Δ12-sets of reals.Jaime I. Ihoda & Saharon Shelah - 1989 - Annals of Pure and Applied Logic 42 (3):207-223.
Δ< sup> 1< sub> 2-sets of reals.Jaime I. Ihoda & Saharon Shelah - 1989 - Annals of Pure and Applied Logic 42 (3):207-223.
The borel conjecture.Haim Judah, Saharon Shelah & W. H. Woodin - 1990 - Annals of Pure and Applied Logic 50 (3):255-269.
DELTA ¹2-sets of reals.J. I. Ihoda - 1989 - Annals of Pure and Applied Logic 42 (3):207.

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Happy families.A. R. D. Mathias - 1977 - Annals of Mathematical Logic 12 (1):59.

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