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The covering number of the strong measure zero ideal can be above almost everything else
- Source :
- Archive for Mathematical Logic. 61:599-610
- Publication Year :
- 2021
- Publisher :
- Springer Science and Business Media LLC, 2021.
-
Abstract
- We show that certain type of tree forcings, including Sacks forcing, increases the covering of the strong measure zero ideal $\mathcal{SN}$. 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 $\mathrm{non}(\mathcal{SN})<br />Comment: 10 pages, 3 figures
- Subjects :
- Logic
010102 general mathematics
Mathematics::General Topology
Mathematics - Logic
0102 computer and information sciences
Covering number
Forcing (mathematics)
Type (model theory)
01 natural sciences
Combinatorics
Null set
Mathematics::Logic
Philosophy
Tree (descriptive set theory)
010201 computation theory & mathematics
FOS: Mathematics
03E17, 03E35, 03E40
Ideal (ring theory)
Continuum (set theory)
0101 mathematics
Invariant (mathematics)
Logic (math.LO)
Mathematics
Subjects
Details
- ISSN :
- 14320665 and 09335846
- Volume :
- 61
- Database :
- OpenAIRE
- Journal :
- Archive for Mathematical Logic
- Accession number :
- edsair.doi.dedup.....9c31d3414fbf4b23951e89df8a4921bd