A mathematical proof of S. Shelah’s theorem on the measure problem and related results
✍ Scribed by Jean Raisonnier
- Book ID
- 112885313
- Publisher
- The Hebrew University Magnes Press
- Year
- 1984
- Tongue
- English
- Weight
- 304 KB
- Volume
- 48
- Category
- Article
- ISSN
- 0021-2172
No coin nor oath required. For personal study only.
📜 SIMILAR VOLUMES
For any integer r \ 1, let a(r) be the largest constant a \ 0 such that if E > 0 and 0 < c < c 0 for some small c 0 =c 0 (r, E) then every graph G of sufficiently large order n and at least edges contains a copy of any (r+1)-chromatic graph H of independence number a(H) [ (a -E) log n log(1/c) .
We employ the probabilistic method to prove a stronger version of a result of Helm, related to a conjecture of Erdos and Turan about additive bases of the positive integers. We show that for a class of random sequences of positive integers \(A\), which satisfy \(|A \cap[1, x]| \gg \sqrt{x}\) with pr