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A NOTE ON PREDICATIVE ORDINAL ANALYSIS I: ITERATED COMPREHENSION AND TRANSFINITE INDUCTION

Published online by Cambridge University Press:  13 February 2019

SATO KENTARO
SATO KENTARO*
Affiliation:
INSTITUTE OF COMPUTER SCIENCE UNIVERSITY OF BERN NEUBRÜCKSTRASSE 10 BERN 3012, SWITZERLANDE-mail: sato@inf.unibe.ch
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Abstract

We determine the proof-theoretic ordinals (i) of ${\cal C} - {\bf{TI}}[\alpha ]$, the transfinite induction along α, for any hyperarithmetical level ${\cal C}$, in the first order setting and (ii) of any combination of iterated arithmetical comprehension and ${\cal C} - {\bf{TI}}[\alpha ]$ for ${\cal C}\, \equiv \,{\rm{\Pi }}_k^i ,{\rm{\Sigma }}_k^i$ ($i\, = \,0,1$) in the second order setting.

Keywords

03F0503F1503F2503F3003F3503D20proof-theoretic ordinalpartial conservationinfinitary semi-formal systemMints’s repetition ruleBuchholz’s finite code of infinitary proofprovably total functionHardy hierarchy
Type
Articles
Information
The Journal of Symbolic Logic , Volume 84 , Issue 1 , March 2019 , pp. 226 - 265
Copyright
Copyright © The Association for Symbolic Logic 2019 

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References

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