Results 11 to 20 of about 33,228 (257)
Ultrafilters in reverse mathematics [PDF]
Journal of Mathematical Logic, 2014 We extend theories of reverse mathematics by a non-principal ultrafilter, and show that these are conservative extensions of the usual theories ACA0, ATR0, and [Formula: see text].
Harvey Friedman, Jeffry L. Hirst
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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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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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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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Splittings and Disjunctions in Reverse Mathematics [PDF]
Notre Dame Journal of Formal Logic, 2020 18 pages, one table, to appear in the Notre Dame Journal for Formal ...
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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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Reverse Mathematics of Matroids [PDF]
, 2016 20 ...
Jeffry L. Hirst, Carl Mummert
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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.
Rupert Hölzl 0001 +2 more
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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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Comput., 2021 Summary: Nets are generalisations of sequences involving possibly \textit{uncountable} index sets; this notion was introduced about a century ago by Moore and Smith. They also established the generalisation to nets of various basic theorems of analysis due to Bolzano-Weierstrass, Dini, Arzelà, and others.
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