Turing degrees in Polish spaces and decomposability of Borel functions

DOI10.1142/S021906132050021XOpenAlexW3010902729MaRDI QIDQ4991901

Keng Meng Ng, Vassilios Gregoriades, Takayuki Kihara

Publication date: 4 June 2021

Published in: Journal of Mathematical Logic (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1410.1052

zbMATH Keywords

Martin conjecturecountably continuous functioncontinuous degreesdecomposability conjectureJayne-Rogers theoremShore-Slaman join theorem

Mathematics Subject Classification ID

Descriptive set theory (03E15) Descriptive set theory (topological aspects of Borel, analytic, projective, etc. sets) (54H05) Applications of computability and recursion theory (03D80)

Related Items (7)

Uniformity results on the Baire property ⋮ A syntactic approach to Borel functions: some extensions of Louveau's theorem ⋮ Descriptive complexity of \(\mathsf{qc} \mathsf{b}_0\)-spaces ⋮ ON A METRIC GENERALIZATION OF THE tt-DEGREES AND EFFECTIVE DIMENSION THEORY ⋮ DECOMPOSING FUNCTIONS OF BAIRE CLASS ON POLISH SPACES ⋮ Point Degree Spectra of Represented Spaces ⋮ Computability of Subsets of Metric Spaces

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Decomposing Borel functions and structure at finite levels of the Baire hierarchy
• First level Borel functions and isomorphisms
• Defining the Turing jump
• Some observations on `A new proof of a theorem of Jayne and Rogers'
• A classification of jump operators
• Effective Borel measurability and reducibility of functions
• Borel isomorphisms at the first level—I
• The space of class $\alpha$ Baire functions
• Decomposing Borel sets and functions and the structure of Baire class 1 functions
• DEFINABILITY OF THE JUMP OPERATOR IN THE ENUMERATION DEGREES
• Decomposing Borel functions using the Shore–Slaman join theorem
• Degrees of unsolvability of continuous functions
• Sigma-continuity with closed witnesses
• Effective decomposition of σ-continuous Borel functions
• On the Structure of Finite Level and ω-Decomposable Borel Functions
• The axiom of determinateness and reduction principles in the analytical hierarchy
• A Separation Theorem for ∑ 1 1 Sets

This page was built for publication: Turing degrees in Polish spaces and decomposability of Borel functions