Journal of Symbolic Logic 64 (2):769-774 (1999)

Abstract
If α and β are ordinals, α ≤ β, and $\beta \nleq \alpha$ , then α + 1 ≤ β. The first result of this paper shows that the restriction of this statement to countable well orderings is provably equivalent to ACA 0 , a subsystem of second order arithmetic introduced by Friedman. The proof of the equivalence is reminiscent of Dekker's construction of a hypersimple set. An application of the theorem yields the equivalence of the set comprehension scheme ACA 0 and an arithmetical transfinite induction scheme
Keywords Reverse Mathematics   Proof Theory
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DOI 10.2307/2586499
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References found in this work BETA

Subsystems of Second-Order Arithmetic.Stephen G. Simpson - 2004 - Studia Logica 77 (1):129-129.
Proof Theory and Logical Complexity.Helmut Pfeifer & Jean-Yves Girard - 1989 - Journal of Symbolic Logic 54 (4):1493.
Reverse Mathematics and Ordinal Exponentiation.Jeffry L. Hirst - 1994 - Annals of Pure and Applied Logic 66 (1):1-18.

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Citations of this work BETA

A Note on Ordinal Exponentiation and Derivatives of Normal Functions.Anton Freund - 2020 - Mathematical Logic Quarterly 66 (3):326-335.
Reverse Mathematics and Rank Functions for Directed Graphs.Jeffry L. Hirst - 2000 - Archive for Mathematical Logic 39 (8):569-579.

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