We show that for every n 1, there exists a 1n -computable family which up to equivalence has exactly one Friedberg numbering which does not induce the least element of the corresponding Rogers semilattice.
Singular systems of linear forms were introduced by Khintchine
in the 1920s, and it was shown by Dani in the 1980s that they
are in one-to-one correspondence with certain divergent orbits of oneparameter
diagonal groups ...
On the space of unimodular lattices, we construct a sequence of
invariant probability measures under a singular diagonal element with high
entropy and show that the limit measure is 0