Wadge reducibility and Hausdorff difference hierarchy in Pω

1981 ◽  
pp. 360-371 ◽  
Author(s):  
A. Tang
Keyword(s):  
Difference Hierarchy ◽  
Wadge Reducibility

scholarly journals On the Wadge Reducibility of k-Partitions

2008 ◽  
Vol 202 ◽  
pp. 59-71 ◽  
Author(s):  
Victor Selivanov
Keyword(s):  
Wadge Reducibility

Equivalence structures and isomorphisms in the difference hierarchy

2009 ◽  
Vol 74 (2) ◽  
pp. 535-556 ◽  
Author(s):  
Douglas Cenzer ◽  
Geoffrey Laforte ◽  
Jeffrey Remmel
Keyword(s):  
Equivalence Relations ◽  
Computable Categoricity ◽  
Difference Hierarchy ◽  
The Difference

AbstractWe examine the effective categoricity of equivalence structures via Ershov's difference hierarchy. We explore various kinds of categoricity available by distinguishing three different notions of isomorphism available in this hierarchy. We prove several results relating our notions of categoricity to computable equivalence relations: for example, we show that, for such relations, computable categoricity is equivalent to our notion of weak ω-c.e. categoricity, and that -categoricity is equivalent to our notion of graph-ω-c.e. categoricity.

scholarly journals Small recursive ordinals, many-one degrees, and the arithmetical difference hierarchy

1975 ◽  
Vol 8 (3) ◽  
pp. 297-343 ◽  
Author(s):  
Louise Hay ◽  
Alfred B. Manaster ◽  
Joseph G. Rosenstein
Keyword(s):  
Difference Hierarchy

Sequential discreteness and clopen-I-Boolean classes

1987 ◽  
Vol 52 (1) ◽  
pp. 232-242
Author(s):  
Randall Dougherty
Keyword(s):  
Final Section ◽  
Baire Space ◽  
Boolean Operations ◽  
Index Set ◽  
Borel Sets ◽  
Borel Hierarchy ◽  
Wadge Reducibility ◽  
Analytic Sets ◽  
Converse Results

Kantorovich and Livenson [6] initiated the study of infinitary Boolean operations applied to the subsets of the Baire space and related spaces. It turns out that a number of interesting collections of subsets of the Baire space, such as the collection of Borel sets of a given type (e.g. the Fσ sets) or the collection of analytic sets, can be expressed as the range of an ω-ary Boolean operation applied to all possible ω-sequences of clopen sets. (Such collections are called clopen-ω-Boolean.) More recently, the ranges of I-ary Boolean operations for uncountable I have been considered; specific questions include whether the collection of Borel sets, or the collection of sets at finite levels in the Borel hierarchy, is clopen-I-Boolean.The main purpose of this paper is to give a characterization of those collections of subsets of the Baire space (or similar spaces) that are clopen-I-Boolean for some I. The Baire space version can be stated as follows: a collection of subsets of the Baire space is clopen-I-Boolean for some I iff it is nonempty and closed downward and σ-directed upward under Wadge reducibility, and in this case we may take I = ω2. The basic method of proof is to use discrete subsets of spaces of the form K2 to put a number of smaller clopen-I-Boolean classes together to form a large one. The final section of the paper gives converse results indicating that, at least in some cases, ω2 cannot be replaced by a smaller index set.

Difference Hierarchy in j-Spaces

2004 ◽  
Vol 43 (4) ◽  
pp. 238-248 ◽  
Author(s):  
V. L. Selivanov
Keyword(s):  
Difference Hierarchy

scholarly journals Towards a descriptive theory of cb0-spaces

2016 ◽  
Vol 27 (8) ◽  
pp. 1553-1580 ◽  
Author(s):  
VICTOR SELIVANOV
Keyword(s):  
Set Theory ◽  
Descriptive Set Theory ◽  
Difference Hierarchy ◽  
Descriptive Theory ◽  
Wadge Hierarchy ◽  
The Difference ◽  
Descriptive Set

The paper tries to extend some results of the classical Descriptive Set Theory to as many countably basedT0-spaces (cb0-spaces) as possible. Along with extending some central facts about Borel, Luzin and Hausdorff hierarchies of sets we also consider the more general case ofk-partitions. In particular, we investigate the difference hierarchy ofk-partitions and the fine hierarchy closely related to the Wadge hierarchy.

Sign in / Sign up

Export Citation Format

Share Document