Reverse Mathematics: Proofs from the Inside Out
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 First edition | |
| Author | John Stillwell |
|---|---|
| Language | English |
| Genre | Mathematics |
| Publisher | Princeton University Press |
Publication date | 2018 |
Reverse Mathematics: Proofs from the Inside Out is a book by John Stillwell on reverse mathematics, the process of examining proofs in mathematics to determine which axioms are required by the proof. It was published in 2018 by the Princeton University Press.[1][2][3][4][5][6]
The book begins with a historical overview of the long struggles with the parallel postulate in Euclidean geometry,[3] and of the foundational crisis of the late 19th and early 20th centuries,[6] Then, after reviewing background material in real analysis and computability theory,[1] the book concentrates on the reverse mathematics of theorems in real analysis,[3] including the Bolzano–Weierstrass theorem, the Heine–Borel theorem, the intermediate value theorem and extreme value theorem, the Heine–Cantor theorem on uniform continuity,[6] the Hahn–Banach theorem, and the Riemann mapping theorem.[5] These theorems are analyzed with respect to three of the "big five" subsystems of second-order arithmetic, namely arithmetical comprehension, recursive comprehension, and the weak Kőnig's lemma.[1]