Variations on Wadge Reducibility Extended Abstract
نویسنده
چکیده
Wadge reducibility in the Baire and Cantor spaces is very important in descriptive set theory. We consider Wadge reducibility in so called φ-spaces which are topological counterpart of the algebraic directed-complete partial orderings. It turns out that in many spaces the Wadge reducibility behaves worse than in the classical case but there exist also interesting examples of spaces with a better behaviour.
منابع مشابه
Wadge Reducibility and Infinite Computations
Introduction Investigation of the infinite behavior of computing devices is of great interest for computer science because many hardware and software concurrent systems (like processors or operating systems) may not terminate. The study of infinite computations is important for several branches of theoretical computer science, including verification and synthesis of reactive computing systems [...
متن کاملA Wadge hierarchy for second countable spaces
Wadge reducibility provides a rich and nice analysis of Borel sets in Polish zero dimensional spaces. However, outside this framework, reducibility by continuous functions was shown to be ill behaved in many important cases. We define a notion of reducibility for subsets of a second countable T0 topological space based on the notions of admissible representations and relatively continuous relat...
متن کاملOn the Wadge reducibility of k-partitions
We establish some results on the Wadge degrees and on the Boolean hierarchy of k-partitions of some spaces, where k is a natural number. The main attention is paid to the Baire space, Baire domain and their close relatives. For the case of Δ2-measurable k-partitions the structures of Wadge degrees are characterized completely. For many degree structures, undecidability of the first-order theori...
متن کاملEarly investigations of the Borel degrees∗
I give an overview/summary of the techniques used, and the results derived, in my 1984 PhD dissertation, Reducibility and Determinateness on the Baire Space. In particular, I focus on the calculation of the order type (and structure) of the collection of degrees of Borel sets.
متن کاملWadge-like reducibilities on arbitrary quasi-Polish spaces
The structure of the Wadge degrees on zero-dimensional spaces is very simple (almost well-ordered), but for many other natural non-zerodimensional spaces (including the space of reals) this structure is much more complicated. We consider weaker notions of reducibility, including the so-called ∆ 0 α-reductions, and try to find for various natural topological spaces X the least ordinal αX such th...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Electr. Notes Theor. Comput. Sci.
دوره 120 شماره
صفحات -
تاریخ انتشار 2005