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Continuous reducibility: functions versus relations

2019
*
Reports on Mathematical Logic
*

It is proved that the Tang-Pequignot reducibility (or reducibility by relatively continuous relations) on

doi:10.4467/20842589rm.19.002.10650
fatcat:ndw24de5a5ekdh6irk52c47lk4
*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). ...##
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Topological Complexity of omega-Powers : Extended Abstract
[article]

2008
*
arXiv
*
pre-print

This is an extended abstract presenting new results on the topological complexity of omega-powers (which are included in

arXiv:0809.1812v1
fatcat:v64qfyhasvhwdoe72lc3ubtp6e
*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*. ...##
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A Q-Wadge Hierarchy in Quasi-Polish Spaces
[article]

2019
*
arXiv
*
pre-print

In fact, many results hold not only

arXiv:1911.02758v1
fatcat:upw6m74aebajjitaamdtsmu6ky
*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*. ...##
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Towards a descriptive set theory for domain-like structures

2006
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Theoretical Computer Science
*

This is

doi:10.1016/j.tcs.2006.07.053
fatcat:zw4tsdo5ozahfpeiyuelgg4mom
*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. ...##
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THE USE OF COMPLEXITY HIERARCHIES IN DESCRIPTIVE SET THEORY AND AUTOMATA THEORY

2005
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TASK Quarterly
*

We discuss in particular the

doaj:0f44ec1146c94f169c29107949943a3f
fatcat:dxvm7dqd4ncdvmbdirup4o7xca
*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*. ...##
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On the Wadge Reducibility of k-Partitions

2008
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Electronical Notes in Theoretical Computer Science
*

We establish some results on the

doi:10.1016/j.entcs.2008.03.008
fatcat:pbjgjwizafdmnch7qeynbrye4m
*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. ...##
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Towards a Descriptive Theory of cb_0-Spaces
[article]

2014
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arXiv
*
pre-print

The paper tries to extend results of the classical Descriptive Set Theory to as many

arXiv:1406.3942v1
fatcat:we7wivsvtrejjm4zoeztsm53sy
*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*). ...##
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On the Wadge reducibility of k-partitions

2010
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The Journal of Logic and Algebraic Programming
*

results on the

doi:10.1016/j.jlap.2009.02.008
fatcat:gkqlz6arwrcabjqavzeg2d4p5m
*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. ...##
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Wadge-like reducibilities on arbitrary quasi-Polish spaces

2014
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Mathematical Structures in Computer Science
*

induced onXby the Δ0β-reductions is simple (i.e. similar to the

doi:10.1017/s0960129513000339
fatcat:5zxl3cp6sbbjdp4cccjkeccqsu
*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*. ...##
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Wadge hardness in Scott spaces and its effectivization

2014
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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. ...

##
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Well Quasiorders and Hierarchy Theory
[article]

2018
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arXiv
*
pre-print

We discuss some applications of WQOs to several fields were

arXiv:1809.02941v1
fatcat:7ztqokcr7ret3fiusnzszegyxa
*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. ...##
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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. ...##
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A Tentative Approach for the Wadge-Wagner Hierarchy of Regular Tree Languages of Index [0, 2]
[chapter]

2015
*
Lecture Notes in Computer Science
*

We provide

doi:10.1007/978-3-319-19225-3_7
fatcat:z6d2m2dhorgfzfxx2c2sx2v2si
*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 ...##
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Interstructure Lattices and Types of Peano Arithmetic, The Graduate Center, City University of New York, USA, 2017. Supervised by Roman Kossak

2018
*
Bulletin of Symbolic Logic
*

THESIS ABSTRACTS

doi:10.1017/bsl.2018.48
fatcat:zmeqvud6efdovflctk5gxasznm
*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*. ...##
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Classification of the spaces Cp⁎(X) within the Borel–Wadge hierarchy for a projective space X

2015
*
Topology and its Applications
*

This completes under the assumption of PD the classification of Borel-

doi:10.1016/j.topol.2014.12.021
fatcat:zbvnlokyknc2fd6jvfai7dap4i
*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. ...
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