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Continuous reducibility: functions versus relations

Riccardo Camerlo
2019 Reports on Mathematical Logic  
It is proved that the Tang-Pequignot reducibility (or reducibility by relatively continuous relations) on a second countable, T0 space X either coincides with the Wadge reducibility for the given topology  ...  , or there is no topology on X that can turn it into Wadge reducibility.  ...  The Wadge hierarchy on a countable space with the cofinite topology (Example 5.3).  ... 
doi:10.4467/20842589rm.19.002.10650 fatcat:ndw24de5a5ekdh6irk52c47lk4

Topological Complexity of omega-Powers : Extended Abstract [article]

Olivier Finkel
2008 arXiv   pre-print
This is an extended abstract presenting new results on the topological complexity of omega-powers (which are included in a paper "Classical and effective descriptive complexities of omega-powers" available  ...  We define now the Borel Hierarchy on a topological space X: Definition 1.  ...  We consider also the Wadge hierarchy which is a great refinement of the Borel hierarchy.  ... 
arXiv:0809.1812v1 fatcat:v64qfyhasvhwdoe72lc3ubtp6e

A Q-Wadge Hierarchy in Quasi-Polish Spaces [article]

Victor Selivanov
2019 arXiv   pre-print
In fact, many results hold not only for the Wadge hierarchy of sets but also for its extension to Borel functions from a space to a countable better quasiorder Q.  ...  The Wadge hierarchy was originally defined and studied only in the Baire space (and some other zero-dimensional spaces).  ...  In this paper we attempt to find the "correct" extension of the Wadge hierarchy from Polish zero-dimensional spaces to arbitrary second countable spaces.  ... 
arXiv:1911.02758v1 fatcat:upw6m74aebajjitaamdtsmu6ky

Towards a descriptive set theory for domain-like structures

Victor L. Selivanov
2006 Theoretical Computer Science  
This is a survey of results in descriptive set theory for domains and similar spaces, with the emphasis on the -algebraic domains.  ...  I am grateful to the university for supporting my stays and to Dieter Spreen for making the stays possible. I thank also an anonymous referee for the careful reading and useful remarks.  ...  Spreen for inviting me to submit this paper.  ... 
doi:10.1016/j.tcs.2006.07.053 fatcat:zw4tsdo5ozahfpeiyuelgg4mom


2005 TASK Quarterly  
We discuss in particular the Wadge and Lipschitz hierarchies for subsets of the Baire and Cantor spaces and the hierarchy of Borel reducibility for finitary relations on standard Borel spaces.  ...  The concept of a reduction between subsets of a given space is described, giving rise to various complexity hierarchies, studied both in descriptive set theory and in automata theory.  ...  The Wadge hierarchy Our aim is now to study the hierarchy of Wadge degrees on the Baire space and the Cantor space.  ... 
doaj:0f44ec1146c94f169c29107949943a3f fatcat:dxvm7dqd4ncdvmbdirup4o7xca

On the Wadge Reducibility of k-Partitions

Victor Selivanov
2008 Electronical Notes in Theoretical Computer Science  
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 Δ 0 2 -measurable k-partitions the structures of Wadge degrees are characterized completely.  ...  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.  ... 
doi:10.1016/j.entcs.2008.03.008 fatcat:pbjgjwizafdmnch7qeynbrye4m

Towards a Descriptive Theory of cb_0-Spaces [article]

Victor Selivanov
2014 arXiv   pre-print
The paper tries to extend results of the classical Descriptive Set Theory to as many countably based T_0-spaces (cb_0-spaces) as possible.  ...  In particular, we investigate the difference hierarchy of k-partitions and the fine hierarchy closely related to the Wadge hierarchy.  ...  The reason is that this hierarchy should generalize the Wadge hierarchy which is defined and relatively well understood only for the Baire space (and some other closely related spaces).  ... 
arXiv:1406.3942v1 fatcat:we7wivsvtrejjm4zoeztsm53sy

On the Wadge reducibility of k-partitions

Victor L. Selivanov
2010 The Journal of Logic and Algebraic Programming  
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 0 2 -measurable k-partitions the structures of Wadge degrees are characterized completely.  ...  I am grateful to Dieter Spreen for organizing the stays, hospitality and many helpful discussions.  ... 
doi:10.1016/j.jlap.2009.02.008 fatcat:gkqlz6arwrcabjqavzeg2d4p5m

Wadge-like reducibilities on arbitrary quasi-Polish spaces

2014 Mathematical Structures in Computer Science  
induced onXby the Δ0β-reductions is simple (i.e. similar to the Wadge hierarchy on the Baire space).  ...  The structure of the Wadge degrees on zero-dimensional spaces is very simple (almost well ordered), but for many other natural nonzero-dimensional spaces (including the space of reals) this structure is  ...  R and its powers), and that the Wadge hierarchy can fail to be very good also on extremely simple countable quasi-Polish spaces.  ... 
doi:10.1017/s0960129513000339 fatcat:5zxl3cp6sbbjdp4cccjkeccqsu

Wadge hardness in Scott spaces and its effectivization

2014 Mathematical Structures in Computer Science  
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  ...  Acknowledgements: The authors are indebted to an anonymous referee for a huge number of improvements in our original manuscript.  ... 
doi:10.1017/s0960129513000248 fatcat:alsjcmqztjbqhitovg7vfotko4

Well Quasiorders and Hierarchy Theory [article]

Victor Selivanov
2018 arXiv   pre-print
We discuss some applications of WQOs to several fields were hierarchies and reducibilities are the principal classification tools, notably to Descriptive Set Theory, Computability theory and Automata Theory  ...  While the classical hierarchies of sets usually degenerate to structures very close to ordinals, the extension of them to functions requires more complicated WQOs, and the same applies to reducibilities  ...  I am grateful to Leibniz-Zentrum für Informatik for accepting and taking care of Dagstuhl Seminars 08271, 11411, 15392, 16031 which were important for promoting the topic of this paper.  ... 
arXiv:1809.02941v1 fatcat:7ztqokcr7ret3fiusnzszegyxa

Page 4408 of Mathematical Reviews Vol. , Issue 86j [page]

1986 Mathematical Reviews  
Louveau gives a description of the detailed structure of the Wadge hierarchy of Borel sets.  ...  The family [A] of all continuous inverse images of A C J is called the Wadge class of A. The Wadge hierarchy is obtained by ordering these classes under strict set inclusion.  ... 

A Tentative Approach for the Wadge-Wagner Hierarchy of Regular Tree Languages of Index [0, 2] [chapter]

Jacques Duparc, Kevin Fournier
2015 Lecture Notes in Computer Science  
We provide a hierarchy of tree languages recognised by nondeterministic parity tree automata with priorities in {0, 1, 2}, whose length exceeds the first fixed point of the ε operation (that itself enumerates  ...  We conjecture that, up to Wadge equivalence, it exhibits all regular tree languages of index [0, 2]. 1 We emphasize that this is done without any determinacy principle.  ...  Therefore, there exists a unique ordinal, called the height of the Γ -Wadge hierarchy, and a mapping d Γ W from the Γ -Wadge hierarchy onto its height, called the Wadge rank, such that, for every L, M  ... 
doi:10.1007/978-3-319-19225-3_7 fatcat:z6d2m2dhorgfzfxx2c2sx2v2si

Interstructure Lattices and Types of Peano Arithmetic, The Graduate Center, City University of New York, USA, 2017. Supervised by Roman Kossak

Athar Abdul-Quader
2018 Bulletin of Symbolic Logic  
THESIS ABSTRACTS Second, I argue that there is a close connection between dynamic epistemic logic and logical geometry.  ...  As a further illustration of the philosophical significance of logical geometry, I also develop a theoretical account of the information levels of the Aristotelian relations and diagrams.  ...  Two of the main hierarchies studied are the Borel and the Wadge hierarchies.  ... 
doi:10.1017/bsl.2018.48 fatcat:zmeqvud6efdovflctk5gxasznm

Classification of the spaces Cp⁎(X) within the Borel–Wadge hierarchy for a projective space X

Martin Doležal, Benjamin Vejnar
2015 Topology and its Applications  
This completes under the assumption of PD the classification of Borel-Wadge complexity of C^*_p(X) for X projective.  ...  They also determined under the assumption of projective determinacy (PD) the complexity of C_p(X) for any projective space X and asked whether a similar result holds for C^*_p(X).  ...  In Definitions 1 and 2, we recall the Wadge hierarchy. Definition 2. Let Γ be a class of sets in Polish spaces. Let X be a Polish space and A be a subset of X.  ... 
doi:10.1016/j.topol.2014.12.021 fatcat:zbvnlokyknc2fd6jvfai7dap4i
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