Transfinite induction within Peano arithmetic

Annals of Pure and Applied Logic 76 (3):231-289 (1995)
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Abstract

The relative strengths of first-order theories axiomatized by transfinite induction, for ordinals less-than 0, and formulas restricted in quantifier complexity, is determined. This is done, in part, by describing the provably recursive functions of such theories. Upper bounds for the provably recursive functions are obtained using model-theoretic techniques. A variety of additional results that come as an application of such techniques are mentioned

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10.1016/0168-0072(95)00029-g

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Citations of this work

Slow consistency.Sy-David Friedman, Michael Rathjen & Andreas Weiermann - 2013 - Annals of Pure and Applied Logic 164 (3):382-393.
A model-theoretic approach to ordinal analysis.Jeremy Avigad & Richard Sommer - 1997 - Bulletin of Symbolic Logic 3 (1):17-52.

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References found in this work

Transfinite recursive progressions of axiomatic theories.Solomon Feferman - 1962 - Journal of Symbolic Logic 27 (3):259-316.
Die Widerspruchsfreiheit der reinen Zahlentheorie.Gerhard Gentzen - 1936 - Journal of Symbolic Logic 1 (2):75-75.
Theory of Formal Systems.Raymond M. Smullyan - 1965 - Journal of Symbolic Logic 30 (1):88-90.

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