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The Axiom of Choice in computability theory and Reverse Mathematics with a cameo for the Continuum Hypothesis

https://doi.org/10.1093/logcom/exaa080
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What this work says

Outgoing claims: the papers this work cites, builds on, or argues with.

inferredcites →https://doi.org/10.1002/malq.200310122openalex-snapshot
Uniform versions of some axioms of second order arithmetic
inferredcites →https://doi.org/10.1007/3-540-44622-2_35openalex-snapshot
Elementary Choiceless Constructive Analysis
inferredcites →https://doi.org/10.1007/978-94-015-9757-9_17openalex-snapshot
Constructive Mathematics without Choice
inferredcites →https://doi.org/10.1007/bf02402869openalex-snapshot
Sur les fonctions de n variables complexes
inferredcites →https://doi.org/10.1007/bfb0091894openalex-snapshot
Iterated Inductive Definitions and Subsystems of Analysis: Recent Proof-Theoretical Studies
inferredcites →https://doi.org/10.1007/s001530050103openalex-snapshot
Lebesgue numbers and Atsuji spaces in subsystems of second-order arithmetic
inferredcites →https://doi.org/10.1016/j.apal.2019.05.007openalex-snapshot
The strength of compactness in Computability Theory and Nonstandard Analysis
inferredcites →https://doi.org/10.1016/j.apal.2020.102788openalex-snapshot
Pincherle's theorem in reverse mathematics and computability theory
inferredcites →https://doi.org/10.1016/s0049-237x(13)72052-4openalex-snapshot
Studies in Logic and the Foundations of Mathematics
inferredcites →https://doi.org/10.1016/s0049-237x(98)80020-7openalex-snapshot
Gödel’s Functional (“Dialectica”) Interpretation
inferredcites →https://doi.org/10.1016/s0168-0072(01)00077-xopenalex-snapshot
On uniform weak König's lemma
inferredcites →https://doi.org/10.1017/9781316755983.005openalex-snapshot
Foundational and mathematical uses of higher types
inferredcites →https://doi.org/10.1017/cbo9780511581007openalex-snapshot
Subsystems of Second Order Arithmetic
inferredcites →https://doi.org/10.1017/jsl.2019.69openalex-snapshot
COMPUTABILITY THEORY, NONSTANDARD ANALYSIS, AND THEIR CONNECTIONS
inferredcites →https://doi.org/10.1038/073052b0openalex-snapshot
Proceedings of the London Mathematical Society
inferredcites →https://doi.org/10.1090/s0002-9939-00-05327-2openalex-snapshot
A weak countable choice principle
inferredcites →https://doi.org/10.1090/s0002-9947-1959-0102480-9openalex-snapshot
Recursive functionals and quantifiers of finite types. I
inferredcites →https://doi.org/10.1090/surv/059openalex-snapshot
Consequences of the Axiom of Choice
inferredcites →https://doi.org/10.1142/4361openalex-snapshot
Introduction to Gauge Integrals
inferredcites →https://doi.org/10.1215/00294527-2020-0021openalex-snapshot
Reverse Mathematics of Topology: Dimension, Paracompactness, and Splittings
inferredcites →https://doi.org/10.1215/00294527-2022-0001openalex-snapshot
Representations and the Foundations of Mathematics
inferredcites →https://doi.org/10.2140/pjm.2000.196.213openalex-snapshot
The fundamental theorem of algebra: a constructive development without choice
inferredcites →https://doi.org/10.2307/2273562openalex-snapshot
The countably based functionals
inferredcites →https://doi.org/10.3233/com-170074openalex-snapshot
The Gandy–Hyland functional and a computational aspect of Nonstandard Analysis
inferredcites →https://doi.org/10.3233/com-200321openalex-snapshot
Computability and non-monotone induction
inferredcites →https://doi.org/10.48550/arxiv.1908.05676openalex-snapshot
Plato and the foundations of mathematics
inferredcites →https://doi.org/10.48550/arxiv.1908.05677openalex-snapshot
Lifting countable to uncountable mathematics
inferredcites →https://doi.org/10.48550/arxiv.2007.07560openalex-snapshot
On the uncountability of $\mathbb{R}$
inferredcites →https://doi.org/10.7146/brics.v6i31.20100openalex-snapshot
Foundational and Mathematical Uses of Higher Types
inferredcites →https://doi.org/10.7146/brics.v7i49.20216openalex-snapshot
Higher Order Reverse Mathematics

What points at this work

Incoming claims: where this work appears in other papers’ reference lists and arguments.

inferred← citeshttps://doi.org/10.1007/978-3-030-80049-9_39openalex-snapshot
Splittings and Robustness for the Heine-Borel Theorem
inferred← citeshttps://doi.org/10.1007/978-3-030-93100-1_15openalex-snapshot
Betwixt Turing and Kleene
inferred← citeshttps://doi.org/10.1007/978-3-030-93100-1_18openalex-snapshot
Between Turing and Kleene
inferred← citeshttps://doi.org/10.1007/978-3-031-15298-6_23openalex-snapshot
On the Computational Properties of the Uncountability of the Real Numbers
inferred← citeshttps://doi.org/10.1007/978-3-031-36978-0_4openalex-snapshot
The Non-normal Abyss in Kleene’s Computability Theory
inferred← citeshttps://doi.org/10.1007/978-3-032-31348-5_34openalex-snapshot
On the Computational Properties of Ambivalent Sets and Functions
inferred← citeshttps://doi.org/10.1007/s00153-025-00991-4openalex-snapshot
On sequential theorems in Reverse Mathematics
inferred← citeshttps://doi.org/10.1016/j.apal.2024.103505openalex-snapshot
On the logical and computational properties of the Vitali covering theorem
inferred← citeshttps://doi.org/10.1016/j.ic.2021.104762openalex-snapshot
Lifting proofs from countable to uncountable mathematics
inferred← citeshttps://doi.org/10.1017/jsl.2022.71openalex-snapshot
ON ROBUST THEOREMS DUE TO BOLZANO, WEIERSTRASS, JORDAN, AND CANTOR
inferred← citeshttps://doi.org/10.1017/jsl.2023.65openalex-snapshot
BIG IN REVERSE MATHEMATICS: MEASURE AND CATEGORY
inferred← citeshttps://doi.org/10.1017/jsl.2024.51openalex-snapshot
APPROXIMATION THEOREMS THROUGHOUT REVERSE MATHEMATICS
inferred← citeshttps://doi.org/10.1093/logcom/exac075openalex-snapshot
On the computational properties of basic mathematical notions
inferred← citeshttps://doi.org/10.1093/logcom/exae048openalex-snapshot
On some computational properties of open sets
inferred← citeshttps://doi.org/10.1142/s0219061324500077openalex-snapshot
The Biggest Five of Reverse Mathematics
inferred← citeshttps://doi.org/10.1177/22113568251320082openalex-snapshot
On the computational properties of the Baire category theorem
inferred← citeshttps://doi.org/10.3233/com-200321openalex-snapshot
Computability and non-monotone induction
inferred← citeshttps://doi.org/10.3233/com-210313openalex-snapshot
Countable sets versus sets that are countable in reverse mathematics
inferred← citeshttps://doi.org/10.3233/com-230475openalex-snapshot
Exploring the abyss in Kleene’s computability theory
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