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• # Artykuł - szczegóły

## Fundamenta Mathematicae

2014 | 224 | 1 | 67-95

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.

67-95

wydano
2014

### Twórcy

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