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Parallelizations in Weihrauch Reducibility and Constructive Reverse Mathematics [PDF]

Lecture Notes in Computer Science, 2020
In the framework of finite-type arithmetic, we characterize the notion that an existence statement is primitive recursive Weihrauch reducible to the parallelization of another existence statement by a standard derivability notion in constructive reverse ...
Makoto Fujiwara
exaly   +3 more sources

Splittings and Disjunctions in Reverse Mathematics [PDF]

Notre Dame Journal of Formal Logic, 2018
Reverse Mathematics (RM hereafter) is a program in the foundations of mathematics founded by Friedman and developed extensively by Simpson and others. The aim of RM is to find the minimal axioms needed to prove a theorem of ordinary, i.e.
Sam Sanders
semanticscholar   +6 more sources

Reverse Mathematics of Matroids [PDF]

Computability and Complexity, 2016
Matroids generalize the familiar notion of linear dependence from linear algebra. Following a brief discussion of founding work in computability and matroids, we use the techniques of reverse mathematics to determine the logical strength of some basis ...
J. Hirst, Carl Mummert
semanticscholar   +4 more sources

On sequential theorems in Reverse Mathematics [PDF]

Archive for Mathematical Logic
Many theorems of mathematics have the form that for a certain problem, e.g. a differential equation or polynomial (in)equality, there exists a solution. The sequential version then states that for a sequence of problems, there is a sequence of solutions.
D. Normann, Sam Sanders
semanticscholar   +3 more sources

Reverse Mathematics

Notices of the American Mathematical Society, 2018
Reverse Mathematics is a program in foundations of mathematics initiated by Friedman ([1, 2]) and developed extensively by Simpson ([4]). Its aim is to determine which minimal axioms prove theorems of ordinary mathematics. Nonstandard methods have played
Carl Mummert
semanticscholar   +2 more sources

BIG IN REVERSE MATHEMATICS: MEASURE AND CATEGORY [PDF]

Journal of Symbolic Logic (JSL), 2023
The smooth development of large parts of mathematics hinges on the idea that some sets are ‘small’ or ‘negligible’ and can therefore be ignored for a given purpose. The perhaps most famous smallness notion, namely ‘measure zero’, originated with Lebesgue,
Sam Sanders
semanticscholar   +1 more source

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
openaire   +4 more sources

Banach’s theorem in higher-order reverse mathematics [PDF]

De Computis, 2023
In this paper, methods of second-order and higher-order reverse mathematics are applied to versions of a theorem of Banach that extends the Schröder–Bernstein theorem.
J. Hirst, Carl Mummert
semanticscholar   +1 more source

ARROW’S THEOREM, ULTRAFILTERS, AND REVERSE MATHEMATICS [PDF]

The Review of Symbolic Logic, 2023
This paper initiates the reverse mathematics of social choice theory, studying Arrow’s impossibility theorem and related results including Fishburn’s possibility theorem and the Kirman–Sondermann theorem within the framework of reverse mathematics.
Benedict Eastaugh
semanticscholar   +1 more source

APPROXIMATION THEOREMS THROUGHOUT REVERSE MATHEMATICS [PDF]

Journal of Symbolic Logic (JSL), 2023
Reverse Mathematics (RM) is a program in the foundations of mathematics where the aim is to find the minimal axioms needed to prove a given theorem of ordinary mathematics. Generally, the minimal axioms are equivalent to the theorem at hand, assuming a
Sam Sanders
semanticscholar   +1 more source