The covering number of the strong measure zero ideal can be above almost everything else

2019/02/05 by Cardona, Miguel A., Mejía, Diego A., Rivera-Madrid, Ismael E. · 1 citation
#03E17 #03E35 #03E40 #FOS: Mathematics #Logic (math.LO)

paper · doi:10.48550/arxiv.1902.01508

Abstract

We show that certain type of tree forcings, including Sacks forcing, increases the covering of the strong measure zero ideal SN. As a consequence, in Sacks model, such covering number is equal to the size of the continuum, which indicates that this covering number is consistently larger than any other classical cardinal invariant of the continuum. Even more, Sacks forcing can be used to force that non(SN)

Cited by

• Directed schemes of ideals and cardinal characteristics, I: the meager additive ideal

Related

• Separating cardinal characteristics of the strong measure zero ideal
• Sacks Forcing and the Shrink Wrapping Property
• More separations of cardinal characteristics of the strong measure zero ideal
• On cardinal characteristics associated with the strong measure zero ideal
• Forcing Diamond and Applications to Iterability