We show that every generalized high Turing degree is the join of two minimal degrees, thereby settling a conjecture of Posner’s from the 70s.

A major focus of research in computability theory in recent years has involved definability issues in degree structures. There has been much success in getting general results by coding methods that translate first or second order arithmetic into the structures. In this paper we concentrate on the issues of getting definitions of interesting, apparently external, relations on degrees that are o...

Throughout the paper, an analytic field means a non-archimedean complete real-valued field, and our main objective is to extend basic theory of transcendental extensions these fields. One easily introduces topological analogue transcendence degree, but, surprisingly, it turns out that may behave very badly. For example, particular case theorem Matignon-Reversat, [8, Thèoréme 2] , asserts if cha...

We introduce Chern degree functions for complexes of coherent sheaves on a polarized surface, which encode information given by stability conditions the boundary $(\alpha, \beta)$-plane. prove that these extend to continuous real valued and we study their differentiability in terms stability. For abelian surfaces, coincide with cohomological rank defined Jiang-Pareschi. illustrate some geometri...