We show that the set of absolutely normal numbers is Π03-complete in the Borel hierarchy of subsets of real numbers. Similarly, the set of absolutely normal numbers is Π03-complete in the effective Borel hierarchy.

We prove that the relation of bisimilarity between countable labelled transition systems (LTS) is Σ1 1-complete (hence not Borel), by reducing the set of non-well orders over the natural numbers continuously to it. This ...

What parts of the classical descriptive set theory done in Polish spaces still hold for more general topological spaces, possibly T0 or T1, but not T2 (i.e. not Hausdorff)? This question has been addressed by Selivanov in ...

In this paper a commuting hierarchy of flows including the full Kostant-Toda equation is studied. A Mulase’s approach which uses the so-called Borel-Gauss decomposition leads to explicit rational solutions of the full ...

We prove some results on the Wadge order on the space of sets of natural numbers endowed with Scott topology, and more generally, on omega-continuous domains. Using alternating decreasing chains we characterize the property ...

It is shown how the complex sine-Gordon equation arises as a symmetry flow of the AKNS hierarchy. The AKNS hierarchy is extended by the 'negative' symmetry flows forming the Borel loop algebra. The complex sine-Gordon and ...

It is shown how the complex sine-Gordon equation arises as a symmetry flow of the AKNS hierarchy. The AKNS hierarchy is extended by the 'negative' symmetry flows forming the Borel loop algebra. The complex sine-Gordon and ...

We demonstrate the full logical independence of normality to multiplicatively independent bases. This establishes that the set of bases to which a real number can be normal is not tied to any arithmetical properties other ...