Counting the changes of random Δ20 sets

• Autores: Figueira, Santiago; Hirschfeldt, Denis R.; Miller, Joseph S.; Ng, Keng Meng; Nies, André
• Año de publicación: 2013
• Idioma: inglés
• Tipo de recurso: artículo
• Materia: MARTIN-LÖF RANDOMNESS; DEMUTH RANDOMNESS; COMPUTABLE APPROXIMATION; OMEGA-C.E.
• Institución: Consejo Nacional de Investigaciones Científicas y Técnicas

We study the number of changes of the initial segment Zs ↾n for computable approximations of a Martin-Löf random Δ02Δ20 set Z. We establish connections between this number of changes and various notions of computability theoretic lowness, as well as the fundamental thesis that, among random sets, randomness is antithetical to computational power. We introduce a new randomness notion, called balanced randomness, which implies that for each computable approximation and each constant c, there are infinitely many n such that Zs ↾n changes more than c2n times. We establish various connections with ω-c.e. tracing and omega;-c.e. jump domination, a new lowness property. We also examine some relationships to randomness theoretic notions of highness, and give applications to the study of (weak) Demuth cuppability.
Fil: Figueira, Santiago. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Computación; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Fil: Hirschfeldt, Denis R.. University of Chicago; Estados Unidos
Fil: Miller, Joseph S.. University of Wisconsin; Estados Unidos
Fil: Ng, Keng Meng. Nanyang Technological University; Singapur
Fil: Nies, André. The University Of Auckland; Nueva Zelanda