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• 16:25, 30 August 2023 RhubarbJayde talk contribs created page Second-order arithmetic (Created page with "Second-order arithmetic, denoted \(Z_2\) is an extension of first-order (i.e. Peano) arithmetic by adding additional second-order variables as well as an induction scheme for \(\mathcal{P}(\mathbb{N})\), and a comprehension scheme. Proof-theoretically, \(Z_2\) is a very expressive system, as it can prove the consistency of Peano arithmetic and its extensions via the addition of iterated inductive definitions - an ordinal analysis of \(Z_2\) is considered the holy grail o...") Tag: Visual edit