Pre-compact families of finite sets of integers and weakly null   sequences in Banach spaces
  Two applications of Nash-Williams' theory of barriers to sequences on Banach spaces are presented: The first one is the $c_0$-saturation of $C(K)$, $K$ countable compacta. The second one is the construction of weakly-null sequences generalizing the example of Maurey-Rosenthal. 
Jordi Lopez Abad (ELM), S. Todorcevic (ELM)