Results 11 to 20 of about 3,387,563 (289)
Instance reducibility and Weihrauch degrees [PDF]
Logical Methods in Computer Science, 2022 We identify a notion of reducibility between predicates, called instance reducibility, which commonly appears in reverse constructive mathematics. The notion can be generally used to compare and classify various principles studied in reverse constructive
Andrej Bauer
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THE REVERSE MATHEMATICS OF THE THIN SET AND ERDŐS–MOSER THEOREMS [PDF]
Journal of Symbolic Logic (JSL), 2021 The thin set theorem for n-tuples and k colors ( $\operatorname {\mathrm {\sf {TS}}}^n_k$ ) states that every k-coloring of $[\mathbb {N}]^n$ admits an infinite set of integers H such that $[H]^n$ avoids at least one color.
Lu Liu, Ludovic Patey
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Inductive inference and reverse mathematics
Annals of Pure and Applied Logic, 2016 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
R. Hölzl, Sanjay Jain, F. Stephan
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Reverse mathematics, trichotomy, and dichotomy
Journal of Logic and Analysis, 2012 Using the techniques of reverse mathematics, we analyze the logical strength of statements similar to trichotomy and dichotomy for sequences of reals. Capitalizing on the connection between sequential statements and constructivity, we find computable restrictions of the statements for sequences and constructive restrictions of the original principles ...
François G Dorais +2 more
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Misconceptions about Numbers and Operations–A Case Study of Preschoolers [PDF]
Educational Process: International Journal, 2023 Background/purpose – Investigation into the misconceptions of preschool students in mathematics and their differences between the ages of 4-5 and 5-6 years old helps form appropriate developmental mathematics teaching programs.
Artemis Eleftheriadi, Konstantinos Lavidas, Gerasimos Koustourakis, Stamatis Papadakis
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Algorithm and proof as Ω-invariance and transfer: A new model of computation in nonstandard analysis [PDF]
Electronic Proceedings in Theoretical Computer Science, 2014 We propose a new model of computation based on nonstandard analysis. Intuitively, the role of "algorithm" is played by a new notion of finite procedure, called Omega-invariance and inspired by physics, from nonstandard analysis.
Sam Sanders
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The Axiom of Choice in computability theory and Reverse Mathematics with a cameo for the Continuum Hypothesis [PDF]
Journal of Logic and Computation, 2020 The Axiom of Choice (AC for short) is the most (in)famous axiom of the usual foundations of mathematics, ZFC set theory. The (non-)essential use of AC in mathematics has been well-studied and thoroughly classified.
D. Normann, Sam Sanders
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The Biggest Five of Reverse Mathematics
Journal of Mathematical Logic, 2023 The aim of Reverse Mathematics (RM for short) is to find the minimal axioms needed to prove a given theorem of ordinary mathematics. These minimal axioms are almost always equivalent to the theorem, working over the base theory of RM, a weak system of computable mathematics.
Dag Normann, Sam Sanders
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RANDOMNESS NOTIONS AND REVERSE MATHEMATICS [PDF]
The Journal of Symbolic Logic, 2019 AbstractWe investigate the strength of a randomness notion${\cal R}$as a set-existence principle in second-order arithmetic: for eachZthere is anXthat is${\cal R}$-random relative toZ. We show that the equivalence between 2-randomness and being infinitely oftenC-incompressible is provable in$RC{A_0}$.
Nies, A, Shafer, P
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Countable sets versus sets that are countable in reverse mathematics [PDF]
De Computis, 2020 The program Reverse Mathematics (RM for short) seeks to identify the axioms necessary to prove theorems of ordinary mathematics, usually working in the language of second-order arithmetic L 2 .
Sam Sanders
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