Abstract
In a paper of 1929, Banachan d Kuratowski proved–assuming the continuum hypothesis–a combinatorial theorem which implies that there is no non-vanishing σ additive finite measure μ on R which is defined for every set of reals. It will be shown that the combinatorial theorem is equivalent to the existence of a K-Lusin set of size 2ℵ0 and that the existence of such sets is independent of ZFC + ¬CH.
| Original language | English |
|---|---|
| Pages (from-to) | 1223-1231 |
| Number of pages | 9 |
| Journal | Rocky Mountain Journal of Mathematics |
| Volume | 33 |
| Issue number | 4 |
| DOIs | |
| State | Published - 2003 |
Keywords
- Cardinal characteristics
- Combinatorial set theory
- Consistency results
- Continuum hypothesis
- Lusin sets
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