Abstract
A subset of the Cantor cube is null-additive if its algebraic sum with any null set is null. We construct a set of cardinality continuum such that: all continuous images of the set into the Cantor cube are null-additive, it contains a homeomorphic copy of a set that is not null-additive, and it has the property, a strong combinatorial covering property. We also construct a nontrivial subset of the Cantor cube with the property that is not null additive. Set-theoretic assumptions used in our constructions are far milder than used earlier by Galvin-Miller and Bartoszyński-Recław, to obtain sets with analogous properties. We also consider products of Sierpiński sets in the context of combinatorial covering properties.
| Original language | English |
|---|---|
| Pages (from-to) | 1231-1242 |
| Number of pages | 12 |
| Journal | Journal of Symbolic Logic |
| Volume | 87 |
| Issue number | 3 |
| DOIs | |
| State | Published - 15 Sep 2022 |
| Externally published | Yes |
Bibliographical note
Publisher Copyright:© 2022 Authors.
Funding
Acknowledgements The present work is a part of the research Project (RP/CHQMIV/2014/115) initiated and funded by the Geological Survey of India, Kolkata in April 2014. The author would like to thank the Director General of the Geological Survey of India, Kolkata, for his kind permission to publish. Mr. Saikat Dutta of the Central Chemical laboratory is acknowledged for his assistance in digestion of the samples. Finally, Dr. Dipayan Guha, Director of the Geochronology and Isotope Geology Division, is acknowledged for his suggestions in improving the manuscript.
| Funders | Funder number |
|---|---|
| Geological Survey of India |
Keywords
- null sets
- null-additive sets
- selection principles
- γ-property