ON WEIHRAUCH REDUCIBILITY AND INTUITIONISTIC REVERSE MATHEMATICS
Copyright policy )ON WEIHRAUCH REDUCIBILITY AND INTUITIONISTIC REVERSE MATHEMATICS
AbstractWe show that there is a strong connection between Weihrauch reducibility on one hand, and provability in EL0, the intuitionistic version of RCA0, on the other hand. More precisely, we show that Weihrauch reducibility to the composition of finitely many instances of a theorem is captured by provability in EL0 together with Markov’s principle, and that Weihrauch reducibility is captured by an affine subsystem of EL0 plus Markov’s principle.
- University of Wisconsin–Madison United States
- UNIVERSITY OF WISCONSIN-MADISON United States
- University of Wisconsin–Oshkosh United States
03B30, 03B20, 03D30, 03F35, Mathematics - Logic, intuitionistic logic, Foundations of classical theories (including reverse mathematics), Weihrauch reducibility, FOS: Mathematics, Other degrees and reducibilities in computability and recursion theory, reverse mathematics, Logic (math.LO), Subsystems of classical logic (including intuitionistic logic), Second- and higher-order arithmetic and fragments
03B30, 03B20, 03D30, 03F35, Mathematics - Logic, intuitionistic logic, Foundations of classical theories (including reverse mathematics), Weihrauch reducibility, FOS: Mathematics, Other degrees and reducibilities in computability and recursion theory, reverse mathematics, Logic (math.LO), Subsystems of classical logic (including intuitionistic logic), Second- and higher-order arithmetic and fragments
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