[图书][B] Slicing the truth: On the computable and reverse mathematics of combinatorial principles
DR Hirschfeldt - 2015 - World Scientific
Ramsey's Theorem [166] captures the idea that total disorder is impossible: a sufficiently
large structure will always contain a large ordered substructure. A well-known special case …
large structure will always contain a large ordered substructure. A well-known special case …
Reverse Mathematics
DD Dzhafarov, C Mummert - … , reductions, and proofs, Theory Appl. Comput …, 2022 - Springer
When we set out to write this book in the spring of 2011, the only introduction to reverse
mathematics was Simpson's Subsystems of Second Order Arithmetic [288]. Our motivation …
mathematics was Simpson's Subsystems of Second Order Arithmetic [288]. Our motivation …
Randomness and differentiability
Randomness and differentiability Page 1 TRANSACTIONS OF THE AMERICAN
MATHEMATICAL SOCIETY Volume 368, Number 1, January 2016, Pages 581–605 http://dx.doi.org/10.1090/tran/6484 …
MATHEMATICAL SOCIETY Volume 368, Number 1, January 2016, Pages 581–605 http://dx.doi.org/10.1090/tran/6484 …
On notions of computability-theoretic reduction between principles
DR Hirschfeldt, CG Jockusch Jr - Journal of Mathematical Logic, 2016 - World Scientific
Several notions of computability-theoretic reducibility between Π 2 1 principles have been
studied. This paper contributes to the program of analyzing the behavior of versions of …
studied. This paper contributes to the program of analyzing the behavior of versions of …
On the mathematical and foundational significance of the uncountable
D Normann, S Sanders - Journal of Mathematical Logic, 2019 - World Scientific
We study the logical and computational properties of basic theorems of uncountable
mathematics, including the Cousin and Lindelöf lemma published in 1895 and 1903 …
mathematics, including the Cousin and Lindelöf lemma published in 1895 and 1903 …
The biggest five of reverse mathematics
D Normann, S Sanders - arXiv preprint arXiv:2212.00489, 2022 - arxiv.org
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 …
prove a given theorem of ordinary mathematics. These minimal axioms are almost always …
The weakness of being cohesive, thin or free in reverse mathematics
L Patey - Israel Journal of Mathematics, 2016 - Springer
Informally, a mathematical statement is robust if its strength is left unchanged under
variations of the statement. In this paper, we investigate the lack of robustness of Ramsey's …
variations of the statement. In this paper, we investigate the lack of robustness of Ramsey's …
[HTML][HTML] Pincherle's theorem in reverse mathematics and computability theory
D Normann, S Sanders - Annals of Pure and Applied Logic, 2020 - Elsevier
We study the logical and computational properties of basic theorems of uncountable
mathematics, in particular Pincherle's theorem, published in 1882. This theorem states that a …
mathematics, in particular Pincherle's theorem, published in 1882. This theorem states that a …
On robust theorems due to Bolzano, Weierstrass, Jordan, and Cantor
D Normann, S Sanders - The Journal of Symbolic Logic, 2024 - cambridge.org
Reverse Mathematics (RM hereafter) is a program in the foundations of mathematics where
the aim is to identify the minimal axioms needed to prove a given theorem from ordinary, ie …
the aim is to identify the minimal axioms needed to prove a given theorem from ordinary, ie …
Restrictions of Hindman's Theorem: an overview
L Carlucci - Connecting with Computability: 17th Conference on …, 2021 - Springer
Restrictions of Hindman’s Theorem: An Overview | SpringerLink Skip to main content
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