The open problem regarding the automorphisms of L*(Q_inf)

Abstract: Guichard proved in 1984 that there are countably many automorphisms of the lattice L(Q_inf) of computably enumerable subspaces of Q_inf by proving that the automorphisms are generated  by computable semilinear transformations. The question about the number of automorphisms of the factor-lattice L*(Q_inf) is still open. We will discuss Ash’s conjecture regarding this question and how some of our recent results corroborate this conjecture.