Bad Wadge-like reducibilities on the Baire space

• Autorzy: Luca Motto Ros
• Języki publikacji: EN

Abstrakty

EN

We consider various collections of functions from the Baire space $^{ω}ω$ into itself naturally arising in (effective) descriptive set theory and general topology, including computable (equivalently, recursive) functions, contraction mappings, and functions which are nonexpansive or Lipschitz with respect to suitable complete ultrametrics on $^{ω}ω$ (compatible with its standard topology). We analyze the degree-structures induced by such sets of functions when used as reducibility notions between subsets of $^{ω}ω$, and we show that the resulting hierarchies of degrees are much more complicated than the classical Wadge hierarchy; in particular, they always contain large infinite antichains, and in most cases also infinite descending chains.

Kategorie tematyczne

• 03D55: Hierarchies
• 03E60: Determinacy principles
• 54C10: Special maps on topological spaces (open, closed, perfect, etc.)
• 03D78: Computation over the reals
• 03E15: Descriptive set theory
• 54E40: Special maps on metric spaces

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2014
• Tom: 224
• Numer: 1
• Strony: 67-95

Daty

wydano

2014

Twórcy

autor

Luca Motto Ros

• Mathematisches Institut - Abteilung für Mathematische Logik, Albert-Ludwigs-Universität Freiburg, Eckerstraße 1, D-79104 Freiburg im Breisgau, Germany

Identyfikatory

DOI

10.4064/fm224-1-4