Wadge hardness in Scott spaces and its effectivization

• Autores: Becher, Veronica Andrea; Grigorieff, Serge
• Año de publicación: 2015
• Idioma: inglés
• Tipo de recurso: artículo
• Materia: Wadge reductions; Scott spaces; Borel Hierarchy
• Institución: Consejo Nacional de Investigaciones Científicas y Técnicas

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 of Wadge hardness for the classes of the Hausdorff difference hierarchy (iterated differences of open sets). A similar characterization holds for Wadge one-to-one and finite-to-one completeness. We consider the same questions for the effectivization of the Wadge relation. We also show that for the space of sets of natural numbers endowed with the Scott topology, in each class of the Hausdorff difference hierarchy there are two strictly increasing chains of Wadge degrees of sets properly in that class. The length of these chains is the rank of the considered class, and each element in one chain is incomparable with all the elements in the other chain.
Fil: Becher, Veronica Andrea. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina
Fil: Grigorieff, Serge. Université Paris Diderot - Paris 7; Francia. Centre National de la Recherche Scientifique; Francia