# Set Theory and Logic

## 1410 Submissions

[2] **viXra:1410.0131 [pdf]**
*submitted on 2014-10-22 17:37:47*

### Roughness of Neutrosophic Sets

**Authors:** A. A. Salama, Said Broumi

**Comments:** 5 Pages.

Since the world is full of indeterminacy, the neutrosophics found their place into
contemporary research. In this paper we define rough neutrosophic sets and study their
properties. Some propositions in this notion are proved. Possible application to computer
sciences is touched upon.

**Category:** Set Theory and Logic

[1] **viXra:1410.0022 [pdf]**
*submitted on 2014-10-04 20:57:05*

### A Note on the Length of Maximal Arithmetic Progressions in Random Subsets

**Authors:** Yilun Shang

**Comments:** 6 Pages.

Let $U^{(n)}$ denote the maximal length arithmetic
progression in a non-uniform random subset of $\{0,1\}^n$, where $1$
appears with probability $p_n$. By using dependency graph and
Stein-Chen method, we show that $U^{(n)}-c_n\ln n$ converges in law
to an extreme type distribution with $\ln p_n=-2/c_n$. Similar
result holds for $W^{(n)}$, the maximal length aperiodic arithmetic
progression (mod $n$).

**Category:** Set Theory and Logic