Descriptive complexity of \(\mathsf{qc} \mathsf{b}_0\)-spaces

DOI10.1016/j.tcs.2022.12.016OpenAlexW4312082568MaRDI QIDQ2682909

Victor L. Selivanov

Publication date: 1 February 2023

Published in: Theoretical Computer Science (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.tcs.2022.12.016

zbMATH Keywords

Polish spaceBorel hierarchydomainWadge reducibilityquasi-Polish space\( \mathsf{c} \mathsf{b}_0\)-space\( \mathsf{qc} \mathsf{b}_0\)-space\(h\)-preorder\(Q\)-partitionHausdorff hierarchyLuzin hierarchywell quasiorder

Mathematics Subject Classification ID

Theory of computing (68Qxx)

Cites Work

• Fine hierarchies via Priestley duality
• A Wadge hierarchy for second countable spaces
• Decomposing Borel functions and structure at finite levels of the Baire hierarchy
• Hierarchies of hyperarithmetical sets and functions
• The Hausdorff-Ershov hierarchy in Euclidean spaces
• Towards a descriptive set theory for domain-like structures
• More on Wadge determinacy
• Preservation of the Borel class under countable-compact-covering mappings
• Fine hierarchies and m-reducibilities in theoretical computer science
• A new proof of a theorem of Jayne and Rogers
• New basic result in classical descriptive set theory: preservation of completeness
• Definability in the \(h\)-quasiorder of labeled forests
• First level Borel functions and isomorphisms
• Index sets in the hyperarithmetical hierarchy
• Theory of representations
• Recursion on the countable functionals
• Total sets and objects in domain theory
• Hereditarily effective typestreams
• Total objects in inductively defined types
• Coding in the partial order of enumerable sets
• Closing the gap between the continuous functionals and recursion in \(^3E\)
• Computable structures and the hyperarithmetical hierarchy
• Extended admissibility.
• Continuous reducibility and dimension of metric spaces
• Comparing Cartesian closed categories of (core) compactly generated spaces
• Quasi-Polish spaces
• Some observations on `A new proof of a theorem of Jayne and Rogers'
• Extending Wadge theory to \(k\)-partitions
• Enumerating classes of effective quasi-Polish spaces
• Boole vs Wadge: comparing two basic tools of descriptive set theory
• Some notes on spaces of ideals and computable topology
• Non-collapse of the effective wadge hierarchy
• Computability on quasi-Polish spaces
• On degree spectra of topological spaces
• On a question by Alexey Ostrovsky concerning preservation of completeness
• Maps of Borel sets
• Genericity of weakly computable objects
• The theory of well-quasi-ordering: a frequently discovered concept
• Effective wadge hierarchy in computable quasi-Polish spaces
• Topological reducibilities for discontinuous functions and their structures
• Base-complexity classifications of qcb0-spaces1
• Turing's Legacy
• Equivalence Relations That Are $\Sigma^0_3$ Complete for Computable Reducibility
• Filter spaces and continuous functionals
• Effective Borel measurability and reducibility of functions
• Hierarchies in?-spaces and applications
• Spaces allowing Type‐2 Complexity Theory revisited
• Towards the Effective Descriptive Set Theory
• Resolvable maps preserve complete metrizability
• A Gandy Theorem for Abstract Structures and Applications to First-Order Definability
• Noetherian Spaces in Verification
• Borel-amenable reducibilities for sets of reals
• The sequential topology on is not regular
• ON A QUESTION OF L. V. KELDYSH CONCERNING THE STRUCTURE OF BOREL SETS
• Les propriétés de réduction et de norme pour les classes de Boréliens
• Borel isomorphisms at the first level—I
• Borel isomorphisms at the first level, II
• Countable functionals and the projective hierarchy
• The space of class $\alpha$ Baire functions
• Data Types as Lattices
• The Steel hierarchy of ordinal valued Borel mappings
• Wadge Degrees ofω-Languages of Deterministic Turing Machines
• Memoir on the Analytical Operations and Projective Sets (I)
• Spectral Spaces
• A comparison of concepts from computable analysis and effective descriptive set theory
• A generalization of a theorem of Hurewicz for quasi-Polish spaces
• Borel subsets of the real line and continuous reducibility
• The uniform Martin’s conjecture for many-one degrees
• Characterizations of absolute F σδ-sets
• Sur une généralisation de la notion d'homéomorphie
• Über innere Abbildungen
• Index sets in Ershov's hierarchy
• Fine hierarchies and Boolean terms
• Computably Enumerable Partial Orders
• Non-Hausdorff Topology and Domain Theory
• On the Difference Hierarchy in Countably Based T0-Spaces
• Total Representations
• Decomposing Borel functions using the Shore–Slaman join theorem
• Turing degrees in Polish spaces and decomposability of Borel functions
• Admissibly Represented Spaces and Qcb-Spaces
• Weihrauch Complexity in Computable Analysis
• Wadge-like degrees of Borel bqo-valued functions
• THE WADGE ORDER ON THE SCOTT DOMAIN IS NOT A WELL-QUASI-ORDER
• Overt choice
• Forests describing Wadge degrees and topological Weihrauch degrees of certain classes of functions and relations
• Baire reductions and good Borel reducibilities
• The isometry degree of a computable copy of ℓ p 1
• Hyperprojective hierarchy of qcb0-spaces
• Hierarchies of Δ⁰₂‐measurable k ‐partitions
• Degrees of unsolvability of continuous functions
• Classes of Polish spaces under effective Borel isomorphism
• First Order Theories of Some Lattices of Open Sets
• On the structure of the Wadge degrees of bqo-valued Borel functions
• Isomorphism relations on computable structures
• Classifying countable Boolean terms
• Bad Wadge-like reducibilities on the Baire space
• Computably Isometric Spaces
• On some problems of descriptive set theory in topological spaces
• Recursive metric spaces
• Decidability of Second-Order Theories and Automata on Infinite Trees
• Borel and Hausdorff hierarchies in topological spaces of Choquet games and their effectivization
• Wadge hardness in Scott spaces and its effectivization
• Spatiality of countably presentable locales (proved with the Baire category theorem)
• Wadge-like reducibilities on arbitrary quasi-Polish spaces
• Some hierarchies of QCB₀-spaces
• Undecidability of Some Topological Theories
• DECOMPOSING FUNCTIONS OF BAIRE CLASS ON POLISH SPACES
• Point Degree Spectra of Represented Spaces
• A Separation Theorem for ∑ 1 1 Sets
• A syntactic approach to Borel functions: some extensions of Louveau's theorem
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