Extending antichains in the poset of the finite subsets of omega
Francisco Santiago Nieto-de la Rosa, Ulises Ariet Ramos-Garcia, Ana Lucia Vargas-Sandoval, Dick de Jongh

Abstract:
We prove that, for every antichain A in the poset of the finite subsets of omega, the set of maximal antichains which extend A has finite size or the size of the continuum. As a consequence we prove a conjecture of de Jongh and Vargas-Sandoval about nepfi families of finite languages.