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Comput., 2019 Nets are generalisations of sequences involving possibly 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 ...
Sam Sanders
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Handbook of the History and Philosophy of Mathematical Practice, 2019
Reverse mathematics is a new field that seeks to find the axioms needed to prove given theorems. Reverse mathematics began as a technical field of mathematical logic, but its main ideas have precedents in the ancient field of geometry and the early ...
J. Stillwell
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Reverse mathematics is a new field that seeks to find the axioms needed to prove given theorems. Reverse mathematics began as a technical field of mathematical logic, but its main ideas have precedents in the ancient field of geometry and the early ...
J. Stillwell
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Reverse Mathematics: Problems, Reductions, and Proofs
Theory and Applications of Computability, 2022D. Dzhafarov, Carl Mummert
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Interval Orders and Reverse Mathematics
Notre Dame Journal of Formal Logic, 2007 We study the reverse mathematics of interval orders. We establish the logical strength of the implications between various definitions of the notion of interval order. We also consider the strength of different versions of the characterization theorem for interval orders: a partial order is an interval order if and only if it does not contain $2 \oplus
Alberto Marcone
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Halin's infinite ray theorems: Complexity and reverse mathematics
Journal of Mathematical Logic, 2023Halin [1965] proved that if a graph has $n$ many pairwise disjoint rays for each $n$ then it has infinitely many pairwise disjoint rays. We analyze the complexity of this and other similar results in terms of computable and proof theoretic complexity ...
James S. Barnes, Jun Le Goh, R. Shore
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The binary expansion and the intermediate value theorem in constructive reverse mathematics
Archive for Mathematical Logic, 2018Takako Nemoto +2 more
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Reverse mathematics and colorings of hypergraphs [PDF]
Archive for Mathematical Logic, 2018 Working in subsystems of second order arithmetic, we formulate several representations for hypergraphs. We then prove the equivalence of various vertex coloring theorems to ${\sf WKL}_0$, ${\sf ACA}_0$ and $Π^1_ 1$-${\sf CA}_0$.
Jeffry Hirst
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John Stillwell*Reverse Mathematics: Proofs from the Inside Out
, 2020Reverse mathematics is a programme in mathematical logic, initiated in the mid-1970s, which seeks to determine which axioms are necessary to prove theorems in areas of ordinary mathematics such as real analysis, countable abstract algebra, countably ...
Benedict Eastaugh
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Reverse Mathematics and Ordinal Multiplication
Mathematical Logic Quarterly, 1998AbstractThis paper uses the framework of reverse mathematics to analyze the proof theoretic content of several statements concerning multiplication of countable well‐orderings. In particular, a division algorithm for ordinal arithmetic is shown to be equivalent to the subsystem ATR0.
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