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Ordinal inequalities, transfinite induction, and reverse mathematics

Published online by Cambridge University Press:  12 March 2014

Jeffry L. Hirst
Jeffry L. Hirst*
Affiliation:
Department of Mathematical Sciences, Appalachian State University, Boone, NC 28608, E-mail: jlh@math.appstate.edu
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Abstract

If α and β are ordinals, α ≤ β, and β ≰ α 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 ACA0 , 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 ACA0 and an arithmetical transfinite induction scheme.

Keywords

reverse mathematicsproof theory

Information

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 64 , Issue 2 , June 1999 , pp. 769 - 774
Copyright
Copyright © Association for Symbolic Logic 1999

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References

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