Results 21 to 30 of about 3,387,563 (289)
The Brouwer invariance theorems in reverse mathematics
Forum of Mathematics, Sigma, 2020 In [12], John Stillwell wrote, ‘finding the exact strength of the Brouwer invariance theorems seems to me one of the most interesting open problems in reverse mathematics.’ In this article, we solve Stillwell’s problem by showing that (some forms of) the
Takayuki Kihara
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What is effective transfinite recursion in reverse mathematics? [PDF]
Mathematical Logic Quarterly, 2020 In the context of reverse mathematics, effective transfinite recursion refers to a principle that allows us to construct sequences of sets by recursion along arbitrary well orders, provided that each set is Δ10 ‐definable relative to the previous stages ...
Anton Freund
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COVID Learning Loss: A Call to Action
Numeracy, 2023 The COVID-19 pandemic and policy responses designed to mitigate transmission have caused deep and persistent mathematics learning loss among K–12 students.
Nathan Grawe
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The modal logic of Reverse Mathematics [PDF]
Archive for Mathematical Logic, 2015 The implication relationship between subsystems in Reverse Mathematics has an underlying logic, which can be used to deduce certain new Reverse Mathematics results from existing ones in a routine way. We use techniques of modal logic to formalize the logic of Reverse Mathematics into a system that we name s-logic.
Carl Mummert +2 more
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The computational content of Nonstandard Analysis [PDF]
Electronic Proceedings in Theoretical Computer Science, 2016 Kohlenbach's proof mining program deals with the extraction of effective information from typically ineffective proofs. Proof mining has its roots in Kreisel's pioneering work on the so-called unwinding of proofs.
Sam Sanders
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The Digital and the Real Universe Foundations of Natural Philosophy and Computational Physics
Philosophies, 2019 In the age of digitization, the world seems to be reducible to a digital computer. However, mathematically, modern quantum field theories do not only depend on discrete, but also continuous concepts.
Klaus Mainzer
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Reverse Mathematics in Bishop’s Constructive Mathematics
Philosophia Scientiæ, 2006 We will overview the results in an informal approach to constructive reverse mathematics, that is reverse mathematics in Bishop’s constructive mathematics, especially focusing on compactness properties and continuous properties.
Hajime Ishihara
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Foundations of Online Structure Theory II: The Operator Approach [PDF]
Logical Methods in Computer Science, 2021 We introduce a framework for online structure theory. Our approach generalises notions arising independently in several areas of computability theory and complexity theory.
Rod Downey +2 more
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Reverse mathematics of regular countable second countable spaces [PDF]
Journal of Symbolic Logic (JSL)We study the reverse mathematics of characterization theorems of regular countable second countable spaces (or $CSCS$ for short). We prove that arithmetic comprehension is equivalent over $\textbf{RCA}_0$ to every $T_3$ $CSCS$ being metrizable, and we ...
G. Genovesi
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Open sets in computability theory and reverse mathematics [PDF]
Journal of Logic and Computation, 2019 To enable the study of open sets in computational approaches to mathematics, lots of extra data and structure on these sets is assumed. For both foundational and mathematical reasons, it is then a natural question, and the subject of this paper, what the
D. Normann, Sam Sanders
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