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- W4310631283 abstract "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. The Big Five phenomenon of RM is the observation that a large number of theorems from ordinary mathematics are either provable in the base theory or equivalent to one of only four systems; these five systems together are called the 'Big Five'. The aim of this paper is to greatly extend the Big Five phenomenon as follows: there are two supposedly fundamentally different approaches to RM where the main difference is whether the language is restricted to second-order objects or if one allows third-order objects. In this paper, we unite these two strands of RM by establishing numerous equivalences involving the second-order Big Five systems on one hand, and well-known third-order theorems from analysis about (possibly) discontinuous functions on the other hand. We both study relatively tame notions, like cadlag or Baire 1, and potentially wild ones, like quasi-continuity. We also show that slight generalisations and variations of the aforementioned third-order theorems fall far outside of the Big Five." @default.
- W4310631283 created "2022-12-13" @default.
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- W4310631283 date "2022-12-01" @default.
- W4310631283 modified "2023-10-18" @default.
- W4310631283 title "The Biggest Five of Reverse Mathematics" @default.
- W4310631283 doi "https://doi.org/10.48550/arxiv.2212.00489" @default.
- W4310631283 hasPublicationYear "2022" @default.
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